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Gómez CM, Linares R, Rodríguez-Martínez EI, Pelegrina S. Age-related changes in brain oscillatory patterns during an n-back task in children and adolescents. Int J Psychophysiol 2024; 202:112372. [PMID: 38849088 DOI: 10.1016/j.ijpsycho.2024.112372] [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: 02/10/2024] [Revised: 05/15/2024] [Accepted: 05/25/2024] [Indexed: 06/09/2024]
Abstract
The development of brain oscillatory responses and their possible role in the working memory (WM) performance of children, adolescents and young adults was investigated. A set of 0- and 1-back tasks with letter stimuli were administered to a final sample of 131 subjects (between 6 and 20 years of age). A decrease in response times (RTs) and an increase of the sensitivity index d-prime (d') were seen with increased age. RTs increased and d' decreased with load, indicating higher difficulty for higher loads. Event-related synchronization (ERS) and event-related desynchronization (ERD) were obtained by the convolution of Morlet wavelets on the recorded EEG. Statistical analyses were performed of the absolute and relative power of brain oscillations defined by topography, frequency and latency. Posterior alpha and beta ERD, and frontocentral theta ERS, were induced by the stimuli presented during the n-back task. While relative theta ERS increased with age, absolute theta ERS, absolute and relative alpha and, absolute beta ERD, decreased with age. Age-related improvement in behavioral performance was mediated by relative theta. Alpha and beta ERD were more pronounced for the most difficult task (1-back) and for the target condition. Globally, there was high consistency of the effects of target type and task load across development. Theta ERS maturation is a crucial step for improving WM performance during development, while alpha and beta ERD maturation seem to be less critical for behavioral performance improvement with age, possibly due to a sufficient level of alpha-beta ERD for good performance in young children.
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Affiliation(s)
- Carlos M Gómez
- University of Sevilla, Experimental Psychology Department, Human Psychobiology Lab., Sevilla, Spain
| | - Rocío Linares
- University of Jaén, Department of Psychology, Jaén, Spain
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2
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Bipul MRS, Rahman MA, Hossain MF. Study on different brain activation rearrangement during cognitive workload from ERD/ERS and coherence analysis. Cogn Neurodyn 2024; 18:1709-1732. [PMID: 39104686 PMCID: PMC11297888 DOI: 10.1007/s11571-023-10032-6] [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: 09/21/2022] [Revised: 07/11/2023] [Accepted: 11/04/2023] [Indexed: 08/07/2024] Open
Abstract
The functional activities of the brain during any task like imaginary, motor, or cognitive are different in pattern as well as their area of activation in the brain is also different. This variation in pattern is also found in the brain's electrical variations that can be measured from the scalp of the brain using an electroencephalogram (EEG). This work exclusively studied a group of subjects' EEG data (available at: https://archive.physionet.org/physiobank/database/eegmat/) to unravel the activation pattern of the human brain during a mental arithmetic task. Since any cognitive task creates variations in EEG signal pattern, the relative changes in the signal power also occur which is also known as event-related desynchronization/synchronization (ERD/ERS). In this work, ERD/ERS have calculated the band-wise power spectral density (PSD) using Welch's method from the EEG signals. Besides, the coherence analysis was also performed to verify the results of ERD/ERS analysis from several randomly chosen subjects' EEG data. Here, subjects performing mental arithmetic tasks were grouped based on their performances: good (subtraction solved > 10 on average) and bad (subtraction solved ≤ 10 on average) to conduct group-specific ERD/ERS analysis regarding their performance in cognitive tasks. It was found that when the brain is on count condition, the variations found in the band power of theta and beta. The amounts of ERS in the left hemisphere are increased. When the task complexity increases, it contributes to an increase in relative ERD/ERS amounts and durations. The left and right hemispheres were asymmetrically distributed by both the pre-stimulus stages of the corresponding band power and relative ERD/ERS.
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Affiliation(s)
- Md. Rayahan Sarker Bipul
- Department of Biomedical Engineering, Khulna University of Engineering and Technology (KUET), Khulna, 9203 Bangladesh
| | - Md. Asadur Rahman
- Department of Biomedical Engineering, Military Institute of Science and Technology (MIST), Mirpur Cantonment, Dhaka, 1216 Bangladesh
| | - Md. Foisal Hossain
- Department of Electronics and Communication Engineering, Khulna University of Engineering and Technology (KUET), Khulna, 9203 Bangladesh
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3
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Song D, Chung DW, Ermentrout GB. Mean-field analysis of synaptic alterations underlying deficient cortical gamma oscillations in schizophrenia. RESEARCH SQUARE 2024:rs.3.rs-3938805. [PMID: 38410475 PMCID: PMC10896366 DOI: 10.21203/rs.3.rs-3938805/v1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/28/2024]
Abstract
Deficient gamma oscillations in the prefrontal cortex (PFC) of individuals with schizophrenia (SZ) are proposed to arise from alterations in the excitatory drive to fast-spiking interneurons ( E → I ) and in the inhibitory drive from these interneurons to excitatory neurons ( I → E ) . Consistent with this idea, prior postmortem studies showed lower levels of molecular and structural markers for the strength of E → I and I → E synapses and also greater variability in E → I synaptic strength in PFC of SZ. Moreover, simulating these alterations in a network of quadratic integrate-and-fire (QIF) neurons revealed a synergistic effect of their interactions on reducing gamma power. In this study, we aimed to investigate the dynamical nature of this synergistic interaction at macroscopic level by deriving a mean-field description of the QIF model network that consists of all-to-all connected excitatory neurons and fast-spiking interneurons. Through a series of numerical simulations and bifurcation analyses, findings from our mean-field model showed that the macroscopic dynamics of gamma oscillations are synergistically disrupted by the interactions among lower strength of E → I and I → E synapses and greater variability in E → I synaptic strength. Furthermore, the two-dimensional bifurcation analyses showed that this synergistic interaction is primarily driven by the shift in Hopf bifurcation due to lower E → I synaptic strength. Together, these simulations predict the nature of dynamical mechanisms by which multiple synaptic alterations interact to robustly reduce PFC gamma power in SZ, and highlight the utility of mean-field model to study macroscopic neural dynamics and their alterations in the illness.
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Affiliation(s)
- Deying Song
- Joint Program in Neural Computation and Machine Learning, Neuroscience Institute, and Machine Learning Department, Carnegie Mellon University, Pittsburgh, PA, USA, 15213
- Center for the Neural Basis of Cognition, University of Pittsburgh, Pittsburgh, PA, USA, 15213
| | - Daniel W. Chung
- Translational Neuroscience Program, Department of Psychiatry, University of Pittsburgh, Pittsburgh, PA, USA, 15213
| | - G. Bard Ermentrout
- Center for the Neural Basis of Cognition, University of Pittsburgh, Pittsburgh, PA, USA, 15213
- Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, USA, 15213
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4
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Gast R, Solla SA, Kennedy A. Neural heterogeneity controls computations in spiking neural networks. Proc Natl Acad Sci U S A 2024; 121:e2311885121. [PMID: 38198531 PMCID: PMC10801870 DOI: 10.1073/pnas.2311885121] [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: 07/12/2023] [Accepted: 11/27/2023] [Indexed: 01/12/2024] Open
Abstract
The brain is composed of complex networks of interacting neurons that express considerable heterogeneity in their physiology and spiking characteristics. How does this neural heterogeneity influence macroscopic neural dynamics, and how might it contribute to neural computation? In this work, we use a mean-field model to investigate computation in heterogeneous neural networks, by studying how the heterogeneity of cell spiking thresholds affects three key computational functions of a neural population: the gating, encoding, and decoding of neural signals. Our results suggest that heterogeneity serves different computational functions in different cell types. In inhibitory interneurons, varying the degree of spike threshold heterogeneity allows them to gate the propagation of neural signals in a reciprocally coupled excitatory population. Whereas homogeneous interneurons impose synchronized dynamics that narrow the dynamic repertoire of the excitatory neurons, heterogeneous interneurons act as an inhibitory offset while preserving excitatory neuron function. Spike threshold heterogeneity also controls the entrainment properties of neural networks to periodic input, thus affecting the temporal gating of synaptic inputs. Among excitatory neurons, heterogeneity increases the dimensionality of neural dynamics, improving the network's capacity to perform decoding tasks. Conversely, homogeneous networks suffer in their capacity for function generation, but excel at encoding signals via multistable dynamic regimes. Drawing from these findings, we propose intra-cell-type heterogeneity as a mechanism for sculpting the computational properties of local circuits of excitatory and inhibitory spiking neurons, permitting the same canonical microcircuit to be tuned for diverse computational tasks.
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Affiliation(s)
- Richard Gast
- Department of Neuroscience, Feinberg School of Medicine, Northwestern University, Chicago, IL60611
- Aligning Science Across Parkinson’s Collaborative Research Network, Chevy Chase, MD20815
| | - Sara A. Solla
- Department of Neuroscience, Feinberg School of Medicine, Northwestern University, Chicago, IL60611
| | - Ann Kennedy
- Department of Neuroscience, Feinberg School of Medicine, Northwestern University, Chicago, IL60611
- Aligning Science Across Parkinson’s Collaborative Research Network, Chevy Chase, MD20815
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5
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Laing CR, Omel’chenko OE. Periodic solutions in next generation neural field models. BIOLOGICAL CYBERNETICS 2023; 117:259-274. [PMID: 37535104 PMCID: PMC10600056 DOI: 10.1007/s00422-023-00969-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/24/2023] [Accepted: 07/12/2023] [Indexed: 08/04/2023]
Abstract
We consider a next generation neural field model which describes the dynamics of a network of theta neurons on a ring. For some parameters the network supports stable time-periodic solutions. Using the fact that the dynamics at each spatial location are described by a complex-valued Riccati equation we derive a self-consistency equation that such periodic solutions must satisfy. We determine the stability of these solutions, and present numerical results to illustrate the usefulness of this technique. The generality of this approach is demonstrated through its application to several other systems involving delays, two-population architecture and networks of Winfree oscillators.
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Affiliation(s)
- Carlo R. Laing
- School of Mathematical and Computational Sciences, Massey University, Private Bag 102-904 NSMC, Auckland, New Zealand
| | - Oleh E. Omel’chenko
- Institute of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam, Germany
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6
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Sawicki J, Berner R, Loos SAM, Anvari M, Bader R, Barfuss W, Botta N, Brede N, Franović I, Gauthier DJ, Goldt S, Hajizadeh A, Hövel P, Karin O, Lorenz-Spreen P, Miehl C, Mölter J, Olmi S, Schöll E, Seif A, Tass PA, Volpe G, Yanchuk S, Kurths J. Perspectives on adaptive dynamical systems. CHAOS (WOODBURY, N.Y.) 2023; 33:071501. [PMID: 37486668 DOI: 10.1063/5.0147231] [Citation(s) in RCA: 10] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/20/2023] [Accepted: 05/24/2023] [Indexed: 07/25/2023]
Abstract
Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems, such as the power grid, social, and neural networks, and they form the backbone of closed-loop control strategies and machine learning algorithms. In this article, we provide an interdisciplinary perspective on adaptive systems. We reflect on the notion and terminology of adaptivity in different disciplines and discuss which role adaptivity plays for various fields. We highlight common open challenges and give perspectives on future research directions, looking to inspire interdisciplinary approaches.
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Affiliation(s)
- Jakub Sawicki
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
- Akademie Basel, Fachhochschule Nordwestschweiz FHNW, Leonhardsstrasse 6, 4009 Basel, Switzerland
| | - Rico Berner
- Department of Physics, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
| | - Sarah A M Loos
- DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Mehrnaz Anvari
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
- Fraunhofer Institute for Algorithms and Scientific Computing, Schloss Birlinghoven, 53757 Sankt-Augustin, Germany
| | - Rolf Bader
- Institute of Systematic Musicology, University of Hamburg, Hamburg, Germany
| | - Wolfram Barfuss
- Transdisciplinary Research Area: Sustainable Futures, University of Bonn, 53113 Bonn, Germany
- Center for Development Research (ZEF), University of Bonn, 53113 Bonn, Germany
| | - Nicola Botta
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
- Department of Computer Science and Engineering, Chalmers University of Technology, 412 96 Göteborg, Sweden
| | - Nuria Brede
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
- Department of Computer Science, University of Potsdam, An der Bahn 2, 14476 Potsdam, Germany
| | - Igor Franović
- Scientific Computing Laboratory, Center for the Study of Complex Systems, Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia
| | - Daniel J Gauthier
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
| | - Sebastian Goldt
- Department of Physics, International School of Advanced Studies (SISSA), Trieste, Italy
| | - Aida Hajizadeh
- Research Group Comparative Neuroscience, Leibniz Institute for Neurobiology, Magdeburg, Germany
| | - Philipp Hövel
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
| | - Omer Karin
- Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom
| | - Philipp Lorenz-Spreen
- Center for Adaptive Rationality, Max Planck Institute for Human Development, Lentzeallee 94, 14195 Berlin, Germany
| | - Christoph Miehl
- Akademie Basel, Fachhochschule Nordwestschweiz FHNW, Leonhardsstrasse 6, 4009 Basel, Switzerland
| | - Jan Mölter
- Department of Mathematics, School of Computation, Information and Technology, Technical University of Munich, Boltzmannstraße 3, 85748 Garching bei München, Germany
| | - Simona Olmi
- Akademie Basel, Fachhochschule Nordwestschweiz FHNW, Leonhardsstrasse 6, 4009 Basel, Switzerland
| | - Eckehard Schöll
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
- Akademie Basel, Fachhochschule Nordwestschweiz FHNW, Leonhardsstrasse 6, 4009 Basel, Switzerland
| | - Alireza Seif
- Pritzker School of Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, USA
| | - Peter A Tass
- Department of Neurosurgery, Stanford University School of Medicine, Stanford, California 94304, USA
| | - Giovanni Volpe
- Department of Physics, University of Gothenburg, Gothenburg, Sweden
| | - Serhiy Yanchuk
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
- Department of Physics, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, Telegrafenberg, 14473 Potsdam, Germany
- Department of Physics, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
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7
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Klinshov VV, Smelov PS, Kirillov SY. Constructive role of shot noise in the collective dynamics of neural networks. CHAOS (WOODBURY, N.Y.) 2023; 33:2894498. [PMID: 37276575 DOI: 10.1063/5.0147409] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2023] [Accepted: 05/18/2023] [Indexed: 06/07/2023]
Abstract
Finite-size effects may significantly influence the collective dynamics of large populations of neurons. Recently, we have shown that in globally coupled networks these effects can be interpreted as additional common noise term, the so-called shot noise, to the macroscopic dynamics unfolding in the thermodynamic limit. Here, we continue to explore the role of the shot noise in the collective dynamics of globally coupled neural networks. Namely, we study the noise-induced switching between different macroscopic regimes. We show that shot noise can turn attractors of the infinitely large network into metastable states whose lifetimes smoothly depend on the system parameters. A surprising effect is that the shot noise modifies the region where a certain macroscopic regime exists compared to the thermodynamic limit. This may be interpreted as a constructive role of the shot noise since a certain macroscopic state appears in a parameter region where it does not exist in an infinite network.
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Affiliation(s)
- V V Klinshov
- Institute of Applied Physics of the Russian Academy of Sciences, Ulyanova Street 46, 603950 Nizhny Novgorod, Russia
- National Research University Higher School of Economics, 25/12 Bol'shaya Pecherskaya Street, Nizhny Novgorod 603155, Russia
| | - P S Smelov
- Institute of Applied Physics of the Russian Academy of Sciences, Ulyanova Street 46, 603950 Nizhny Novgorod, Russia
| | - S Yu Kirillov
- Institute of Applied Physics of the Russian Academy of Sciences, Ulyanova Street 46, 603950 Nizhny Novgorod, Russia
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8
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Kheirabadi NR, Chiolerio A, Szaciłowski K, Adamatzky A. Neuromorphic Liquids, Colloids, and Gels: A Review. Chemphyschem 2023; 24:e202200390. [PMID: 36002385 PMCID: PMC10092099 DOI: 10.1002/cphc.202200390] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2022] [Revised: 08/23/2022] [Indexed: 01/07/2023]
Abstract
Advances in flexible electronic devices and robotic software require that sensors and controllers be virtually devoid of traditional electronic components, be deformable and stretch-resistant. Liquid electronic devices that mimic biological synapses would make an ideal core component for flexible liquid circuits. This is due to their unbeatable features such as flexibility, reconfiguration, fault tolerance. To mimic synaptic functions in fluids we need to imitate dynamics and complexity similar to those that occurring in living systems. Mimicking ionic movements are considered as the simplest platform for implementation of neuromorphic in material computing systems. We overview a series of experimental laboratory prototypes where neuromorphic systems are implemented in liquids, colloids and gels.
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Affiliation(s)
| | - Alessandro Chiolerio
- Unconventional Computing Laboratory, UWE, Bristol, UK.,Center for Bioinspired Soft Robotics, Istituto Italiano di Tecnologia, Genova, Italy
| | - Konrad Szaciłowski
- Academic Centre for Materials and Nanotechnology, AGH University of Science and Technology, Krakow, Poland
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9
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Zhang J, Zhu C, Han J. The neural mechanism of non-phase-locked EEG activity in task switching. Neurosci Lett 2023; 792:136957. [PMID: 36347341 DOI: 10.1016/j.neulet.2022.136957] [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: 09/12/2022] [Revised: 10/23/2022] [Accepted: 11/01/2022] [Indexed: 11/06/2022]
Abstract
Flexible switching between different tasks is an important cognitive ability for humans and it is often studied using the task-switching paradigm. Although the neural mechanisms of task switching have been extensively explored in previous studies using event-related potentials techniques, the activity and process mechanisms of non-phase-locked electroencephalography (EEG) have rarely been revealed. For this reason, this paper discusses the processing of non-phase-locked EEG oscillations in task switching based on frequency-band delineation. First, the roles of each frequency band in local brain regions were summarized. In particular, during the proactive control process (the cue-stimulus interval), delta, theta, and alpha oscillations played more roles in the switch condition while beta played more roles in repeat task. In the reactive control process (post-target), delta, alpha, and beta are all related to sensorimotor function. Then, utilizing the functional connectivity (FC) method, delta connections in the frontotemporal regions and theta connections located in the parietal-to-occipital sites are involved in the preparatory period before task switching, while alpha connections located in the sensorimotor areas and beta connections located in the frontal-parietal cortex are involved in response inhibition. Finally, cross-frequency coupling (CFC) play an important role in working memory among different band oscillation. The present study shows that in addition to the processing mechanisms specific to each frequency band, there are some shared and interactive neural mechanism in task switching by using different analysis techniques.
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Affiliation(s)
- Jing Zhang
- Brain and Cognitive Neuroscience Research Center, Liaoning Normal University, Dalian, China; Key Laboratory of Brain and Cognitive Neuroscience, Liaoning Province, Dalian, China
| | - Chengdong Zhu
- School of Physical Education, Liaoning Normal University, Dalian, China
| | - Jiahui Han
- Brain and Cognitive Neuroscience Research Center, Liaoning Normal University, Dalian, China; Key Laboratory of Brain and Cognitive Neuroscience, Liaoning Province, Dalian, China.
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10
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Klinshov VV, Kirillov SY. Shot noise in next-generation neural mass models for finite-size networks. Phys Rev E 2022; 106:L062302. [PMID: 36671128 DOI: 10.1103/physreve.106.l062302] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2022] [Accepted: 12/12/2022] [Indexed: 06/17/2023]
Abstract
Neural mass models is a general name for various models describing the collective dynamics of large neural populations in terms of averaged macroscopic variables. Recently, the so-called next-generation neural mass models have attracted a lot of attention due to their ability to account for the degree of synchrony. Being exact in the limit of infinitely large number of neurons, these models provide only an approximate description of finite-size networks. In the present Letter we study finite-size effects in the collective behavior of neural networks and prove that these effects can be captured by appropriately modified neural mass models. Namely, we show that the finite size of the network leads to the emergence of the so-called shot noise appearing as a stochastic term in the neural mass model. The power spectrum of this shot noise contains pronounced peaks, therefore its impact on the collective dynamics might be crucial due to resonance effects.
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Affiliation(s)
- Vladimir V Klinshov
- Institute of Applied Physics of the Russian Academy of Sciences, 46 Ul'yanov Street, Nizhny Novgorod 603950, Russia and Faculty of Informatics, Mathematics, and Computer Science, National Research University Higher School of Economics, 25/12 Bol'shaya Pecherskaya Street, Nizhny Novgorod 603155, Russia
| | - Sergey Yu Kirillov
- Institute of Applied Physics of the Russian Academy of Sciences, 46 Ul'yanov Street, Nizhny Novgorod 603950, Russia
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11
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Cross-scale excitability in networks of quadratic integrate-and-fire neurons. PLoS Comput Biol 2022; 18:e1010569. [PMID: 36191049 PMCID: PMC9560555 DOI: 10.1371/journal.pcbi.1010569] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2022] [Revised: 10/13/2022] [Accepted: 09/13/2022] [Indexed: 11/05/2022] Open
Abstract
From the action potentials of neurons and cardiac cells to the amplification of calcium signals in oocytes, excitability is a hallmark of many biological signalling processes. In recent years, excitability in single cells has been related to multiple-timescale dynamics through canards, special solutions which determine the effective thresholds of the all-or-none responses. However, the emergence of excitability in large populations remains an open problem. Here, we show that the mechanism of excitability in large networks and mean-field descriptions of coupled quadratic integrate-and-fire (QIF) cells mirrors that of the individual components. We initially exploit the Ott-Antonsen ansatz to derive low-dimensional dynamics for the coupled network and use it to describe the structure of canards via slow periodic forcing. We demonstrate that the thresholds for onset and offset of population firing can be found in the same way as those of the single cell. We combine theoretical analysis and numerical computations to develop a novel and comprehensive framework for excitability in large populations, applicable not only to models amenable to Ott-Antonsen reduction, but also to networks without a closed-form mean-field limit, in particular sparse networks.
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12
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Reyner-Parra D, Huguet G. Phase-locking patterns underlying effective communication in exact firing rate models of neural networks. PLoS Comput Biol 2022; 18:e1009342. [PMID: 35584147 PMCID: PMC9154197 DOI: 10.1371/journal.pcbi.1009342] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2021] [Revised: 05/31/2022] [Accepted: 04/25/2022] [Indexed: 11/19/2022] Open
Abstract
Macroscopic oscillations in the brain have been observed to be involved in many cognitive tasks but their role is not completely understood. One of the suggested functions of the oscillations is to dynamically modulate communication between neural circuits. The Communication Through Coherence (CTC) theory proposes that oscillations reflect rhythmic changes in excitability of the neuronal populations. Thus, populations need to be properly phase-locked so that input volleys arrive at the peaks of excitability of the receiving population to communicate effectively. Here, we present a modeling study to explore synchronization between neuronal circuits connected with unidirectional projections. We consider an Excitatory-Inhibitory (E-I) network of quadratic integrate-and-fire neurons modeling a Pyramidal-Interneuronal Network Gamma (PING) rhythm. The network receives an external periodic input from either one or two sources, simulating the inputs from other oscillating neural groups. We use recently developed mean-field models which provide an exact description of the macroscopic activity of the spiking network. This low-dimensional mean field model allows us to use tools from bifurcation theory to identify the phase-locked states between the input and the target population as a function of the amplitude, frequency and coherence of the inputs. We identify the conditions for optimal phase-locking and effective communication. We find that inputs with high coherence can entrain the network for a wider range of frequencies. Besides, faster oscillatory inputs than the intrinsic network gamma cycle show more effective communication than inputs with similar frequency. Our analysis further shows that the entrainment of the network by inputs with higher frequency is more robust to distractors, thus giving them an advantage to entrain the network and communicate effectively. Finally, we show that pulsatile inputs can switch between attended inputs in selective attention. Oscillations are ubiquitous in the brain and are involved in several cognitive tasks but their role is not completely understood. The Communication Through Coherence theory proposes that background oscillations in the brain regulate the information flow between neural populations. The oscillators that are properly phase-locked so that inputs arrive at the peaks of excitability of the receiving population communicate effectively. In this paper, we study the emerging phase-locking patterns of a network generating PING oscillations under external periodic forcing, simulating the oscillatory input from other neural groups. We identify the conditions for optimal phase-locking and effective communication. Namely, we find that inputs with higher frequency and coherence have an adavantage to entrain the network and we quantify how robust are to distractors. Furthermore, we show how selective attention can be implemented by means of phase locking and we show that pulsatile inputs can switch between attended inputs.
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Affiliation(s)
- David Reyner-Parra
- Departament de Matemàtiques, Universitat Politècnica de Catalunya, Barcelona, Spain
| | - Gemma Huguet
- Departament de Matemàtiques, Universitat Politècnica de Catalunya, Barcelona, Spain
- Institut de Matemàtiques de la UPC - Barcelona Tech (IMTech), Barcelona, Spain
- Centre de Recerca Matemàtica, Barcelona, Spain
- * E-mail:
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13
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Majhi S. Dynamical robustness of complex networks subject to long-range connectivity. Proc Math Phys Eng Sci 2022. [DOI: 10.1098/rspa.2021.0953] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
In spite of a few attempts in understanding the dynamical robustness of complex networks, this extremely important subject of research is still in its dawn as compared to the other dynamical processes on networks. We hereby consider the concept of long-range interactions among the dynamical units of complex networks and demonstrate
for the first time
that such a characteristic can have noteworthy impacts on the dynamical robustness of networked systems, regardless of the underlying network topology. We present a comprehensive analysis of this phenomenon on top of diverse network architectures. Such dynamical damages being able to substantially affect the network performance, determining mechanisms that boost the robustness of networks becomes a fundamental question. In this work, we put forward a prescription based upon self-feedback that can efficiently resurrect global rhythmicity of complex networks composed of active and inactive dynamical units, and thus can enhance the network robustness. We have been able to delineate the whole proposition analytically while dealing with all
d
-path adjacency matrices, having an excellent agreement with the numerical results. For the numerical computations, we examine scale-free networks, Watts–Strogatz small-world model and also Erdös–Rényi random network, along with Landau–Stuart oscillators for casting the local dynamics.
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Affiliation(s)
- Soumen Majhi
- Department of Mathematics, Bar-Ilan University, Ramat-Gan 5290002, Israel
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14
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Behavior of olfactory-related frontal lobe oscillations in Alzheimer's disease and MCI: A pilot study. Int J Psychophysiol 2022; 175:43-53. [PMID: 35217110 DOI: 10.1016/j.ijpsycho.2022.02.008] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2021] [Revised: 12/19/2021] [Accepted: 02/17/2022] [Indexed: 11/20/2022]
Abstract
Slow-gamma (35-45 Hz) phase synchronization and the coupling between slow-gamma and low-frequency theta oscillations (4-8 Hz) are closely related to memory retrieval and cognitive functions. In this pilot study, we assess the Phase Amplitude Coupling (PAC) between theta and slow-gamma oscillatory bands and the quality of synchronization in slow-gamma oscillations using Phase Locking Value (PLV) on EEG data from healthy individuals and patients diagnosed with amnestic Mild Cognitive Impairment (aMCI) and Alzheimer's Disease (AD) during an oddball olfactory task. Our study indicates noticeable differences between the PLV and PAC values corresponding to olfactory stimulation in the three groups of participants. These differences can help explain the underlying processes involved in these cognitive disorders and the differences between aMCI and AD patients in performing cognitive tasks. Our study also proposes a diagnosis method for aMCI through comparing the brain's response characteristics during olfactory stimulation and rest. Early diagnosis of aMCI can potentially lead to its timely treatment and prevention from progression to AD.
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15
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Spiliotis K, Starke J, Franz D, Richter A, Köhling R. Deep brain stimulation for movement disorder treatment: exploring frequency-dependent efficacy in a computational network model. BIOLOGICAL CYBERNETICS 2022; 116:93-116. [PMID: 34894291 PMCID: PMC8866393 DOI: 10.1007/s00422-021-00909-2] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/20/2020] [Accepted: 10/31/2021] [Indexed: 06/14/2023]
Abstract
A large-scale computational model of the basal ganglia network and thalamus is proposed to describe movement disorders and treatment effects of deep brain stimulation (DBS). The model of this complex network considers three areas of the basal ganglia region: the subthalamic nucleus (STN) as target area of DBS, the globus pallidus, both pars externa and pars interna (GPe-GPi), and the thalamus. Parkinsonian conditions are simulated by assuming reduced dopaminergic input and corresponding pronounced inhibitory or disinhibited projections to GPe and GPi. Macroscopic quantities are derived which correlate closely to thalamic responses and hence motor programme fidelity. It can be demonstrated that depending on different levels of striatal projections to the GPe and GPi, the dynamics of these macroscopic quantities (synchronisation index, mean synaptic activity and response efficacy) switch from normal to Parkinsonian conditions. Simulating DBS of the STN affects the dynamics of the entire network, increasing the thalamic activity to levels close to normal, while differing from both normal and Parkinsonian dynamics. Using the mentioned macroscopic quantities, the model proposes optimal DBS frequency ranges above 130 Hz.
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Affiliation(s)
| | - Jens Starke
- Institute of Mathematics, University of Rostock, 18057 Rostock, Germany
| | - Denise Franz
- Oscar-Langendorff-Institute of Physiology, Rostock University Medical Center, Rostock, Germany
| | - Angelika Richter
- Institute of Pharmacology, Pharmacy and Toxicology, Faculty of Veterinary Medicine, University of Leipzig, Leipzig, Germany
| | - Rüdiger Köhling
- Oscar-Langendorff-Institute of Physiology, Rostock University Medical Center, Rostock, Germany
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16
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Josipovic Z. Implicit-explicit gradient of nondual awareness or consciousness as such. Neurosci Conscious 2021; 2021:niab031. [PMID: 34646576 PMCID: PMC8500298 DOI: 10.1093/nc/niab031] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2021] [Revised: 06/29/2021] [Accepted: 08/19/2021] [Indexed: 01/04/2023] Open
Abstract
Consciousness is multi-dimensional but is most often portrayed with a two-dimensional (2D) map that has global levels or states on one axis and phenomenal contents on the other. On this map, awareness is conflated either with general alertness or with phenomenal content. This contributes to ongoing difficulties in the scientific understanding of consciousness. Previously, I have proposed that consciousness as such or nondual awareness-a basic non-conceptual, non-propositional awareness in itself free of subject-object fragmentation-is a unique kind that cannot be adequately specified by this 2D map of states and contents. Here, I propose an implicit-explicit gradient of nondual awareness to be added as the z-axis to the existing 2D map of consciousness. This gradient informs about the degree to which nondual awareness is manifest in any experience, independent of the specifics of global state or local content. Alternatively, within the multi-dimensional state space model of consciousness, nondual awareness can be specified by several vectors, each representing one of its properties. In the first part, I outline nondual awareness or consciousness as such in terms of its phenomenal description, its function and its neural correlates. In the second part, I explore the implicit-explicit gradient of nondual awareness and how including it as an additional axis clarifies certain features of everyday dualistic experiences and is especially relevant for understanding the unitary and nondual experiences accessed via different contemplative methods, mind-altering substances or spontaneously.
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Affiliation(s)
- Zoran Josipovic
- Psychology Department, Graduate School of Arts & Sciences, New York University, New York, NY 10003, USA
- Nonduality Institute, Woodstock, NY 12498, USA
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17
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Gast R, Gong R, Schmidt H, Meijer HGE, Knösche TR. On the Role of Arkypallidal and Prototypical Neurons for Phase Transitions in the External Pallidum. J Neurosci 2021; 41:6673-6683. [PMID: 34193559 PMCID: PMC8336705 DOI: 10.1523/jneurosci.0094-21.2021] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2021] [Revised: 04/08/2021] [Accepted: 05/13/2021] [Indexed: 01/10/2023] Open
Abstract
The external pallidum (globus pallidus pars externa [GPe]) plays a central role for basal ganglia functions and dynamics and, consequently, has been included in most computational studies of the basal ganglia. These studies considered the GPe as a homogeneous neural population. However, experimental studies have shown that the GPe contains at least two distinct cell types (prototypical and arkypallidal cells). In this work, we provide in silico insight into how pallidal heterogeneity modulates dynamic regimes inside the GPe and how they affect the GPe response to oscillatory input. We derive a mean-field model of the GPe system from a microscopic spiking neural network of recurrently coupled prototypical and arkypallidal neurons. Using bifurcation analysis, we examine the influence of dopamine-dependent changes of intrapallidal connectivity on the GPe dynamics. We find that increased self-inhibition of prototypical cells can induce oscillations, whereas increased inhibition of prototypical cells by arkypallidal cells leads to the emergence of a bistable regime. Furthermore, we show that oscillatory input to the GPe, arriving from striatum, leads to characteristic patterns of cross-frequency coupling observed at the GPe. Based on these findings, we propose two different hypotheses of how dopamine depletion at the GPe may lead to phase-amplitude coupling between the parkinsonian beta rhythm and a GPe-intrinsic γ rhythm. Finally, we show that these findings generalize to realistic spiking neural networks of sparsely coupled Type I excitable GPe neurons.SIGNIFICANCE STATEMENT Our work provides (1) insight into the theoretical implications of a dichotomous globus pallidus pars externa (GPe) organization, and (2) an exact mean-field model that allows for future investigations of the relationship between GPe spiking activity and local field potential fluctuations. We identify the major phase transitions that the GPe can undergo when subject to static or periodic input and link these phase transitions to the emergence of synchronized oscillations and cross-frequency coupling in the basal ganglia. Because of the close links between our model and experimental findings on the structure and dynamics of prototypical and arkypallidal cells, our results can be used to guide both experimental and computational studies on the role of the GPe for basal ganglia dynamics in health and disease.
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Affiliation(s)
- Richard Gast
- Max Planck Institute for Human Cognitive and Brain Sciences, Brain Networks Group, Leipzig, Germany 04103
| | - Ruxue Gong
- Max Planck Institute for Human Cognitive and Brain Sciences, Brain Networks Group, Leipzig, Germany 04103
| | - Helmut Schmidt
- Max Planck Institute for Human Cognitive and Brain Sciences, Brain Networks Group, Leipzig, Germany 04103
| | - Hil G E Meijer
- Department of Applied Mathematics, Technical Medical Centre, University of Twente, Enschede, The Netherlands 7522 NB
| | - Thomas R Knösche
- Max Planck Institute for Human Cognitive and Brain Sciences, Brain Networks Group, Leipzig, Germany 04103
- Institute for Biomedical Engineering and Informatics, Ilmenau, Germany 98684
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18
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Goldobin DS, di Volo M, Torcini A. Reduction Methodology for Fluctuation Driven Population Dynamics. PHYSICAL REVIEW LETTERS 2021; 127:038301. [PMID: 34328756 DOI: 10.1103/physrevlett.127.038301] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2020] [Revised: 03/24/2021] [Accepted: 06/14/2021] [Indexed: 06/13/2023]
Abstract
Lorentzian distributions have been largely employed in statistical mechanics to obtain exact results for heterogeneous systems. Analytic continuation of these results is impossible even for slightly deformed Lorentzian distributions due to the divergence of all the moments (cumulants). We have solved this problem by introducing a "pseudocumulants" expansion. This allows us to develop a reduction methodology for heterogeneous spiking neural networks subject to extrinsic and endogenous fluctuations, thus obtaining a unified mean-field formulation encompassing quenched and dynamical sources of disorder.
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Affiliation(s)
- Denis S Goldobin
- Institute of Continuous Media Mechanics, Ural Branch of RAS, Acad. Korolev Street 1, 614013 Perm, Russia
- Department of Theoretical Physics, Perm State University, Bukirev Street 15, 614990 Perm, Russia
| | - Matteo di Volo
- Laboratoire de Physique Théorique et Modélisation, Université de Cergy-Pontoise, CNRS, UMR 8089, 95302 Cergy-Pontoise cedex, France
| | - Alessandro Torcini
- Laboratoire de Physique Théorique et Modélisation, Université de Cergy-Pontoise, CNRS, UMR 8089, 95302 Cergy-Pontoise cedex, France
- CNR-Consiglio Nazionale delle Ricerche-Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy
- INFN Sezione di Firenze, Via Sansone 1, I-50019 Sesto Fiorentino, Florence, Italy
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19
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Novikov N, Gutkin B. Role of synaptic nonlinearity in persistent firing rate shifts caused by external periodic forcing. Phys Rev E 2021; 101:052408. [PMID: 32575174 DOI: 10.1103/physreve.101.052408] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2019] [Accepted: 03/03/2020] [Indexed: 11/07/2022]
Abstract
Information storage and processing in the brain largely relies on the neural population coding principle. In this framework, information is reflected in the population firing rate that reflects asynchronous irregular spiking of its constituent neurons. Periodic modulations of neural activity can lead to neural activity oscillations. Data indicate that such oscillations are ubiquitous in brain activity and are modulated, in frequency and amplitude, in a functionally meaningful manner. The relationship between oscillations and the population rate code remains an open issue. While ample works show how changes in the mean firing rate may alter neural oscillations, the reverse connection is unclear. One notable possibility is that oscillatory activity impinging on a neural population modulates its mean firing rate, thereby impacting information processing. We suggest that such modulation requires nonlinearities and propose nonlinear excitatory coupling via slow N-methyl-D-aspartate (NMDA) receptors as the prevalent mechanism. The aim of our paper is to theoretically explore to what extent the NMDA-related mechanism could account for oscillation-induced mean firing rate changes. We consider a mean-field model of a neural circuit containing an excitatory and an inhibitory population with linear transfer functions. Along with NMDA excitation, the model included fast recurrent excitatory and inhibitory connectivity. To explicitly study the effects of impinging oscillation on the rate dynamics, we subjected the circuit to a sinusoidal input signal imitating an input from distant brain regions or from a larger network into which the circuit is embedded. Using time-scale separation and time-averaging techniques, we developed a geometric method to determine the oscillation-induced mean firing rate shifts and validated it by numeric simulations of the model. Our results indicate that a large-amplitude stable firing rate shift requires nonlinear NMDA synapses on both the excitatory and the inhibitory populations. Our results delineate specific neural synaptic properties that enable neural oscillations to act as flexible modulators of the population rate code.
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Affiliation(s)
- Nikita Novikov
- Centre for Cognition and Decision Making, National Research University Higher School of Economics, Moscow 101000, Russia
| | - Boris Gutkin
- Centre for Cognition and Decision Making, National Research University Higher School of Economics, Moscow 101000, Russia.,Group for Neural Theory, LNC INSERM U960, Department of Cognitive Studies, Ecole Normale Superieure PSL Research University, Paris 75005, France
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20
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Novikov N, Zakharov D, Moiseeva V, Gutkin B. Activity Stabilization in a Population Model of Working Memory by Sinusoidal and Noisy Inputs. Front Neural Circuits 2021; 15:647944. [PMID: 33967703 PMCID: PMC8096914 DOI: 10.3389/fncir.2021.647944] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/30/2020] [Accepted: 03/19/2021] [Indexed: 01/22/2023] Open
Abstract
According to mechanistic theories of working memory (WM), information is retained as stimulus-dependent persistent spiking activity of cortical neural networks. Yet, how this activity is related to changes in the oscillatory profile observed during WM tasks remains a largely open issue. We explore joint effects of input gamma-band oscillations and noise on the dynamics of several firing rate models of WM. The considered models have a metastable active regime, i.e., they demonstrate long-lasting transient post-stimulus firing rate elevation. We start from a single excitatory-inhibitory circuit and demonstrate that either gamma-band or noise input could stabilize the active regime, thus supporting WM retention. We then consider a system of two circuits with excitatory intercoupling. We find that fast coupling allows for better stabilization by common noise compared to independent noise and stronger amplification of this effect by in-phase gamma inputs compared to anti-phase inputs. Finally, we consider a multi-circuit system comprised of two clusters, each containing a group of circuits receiving a common noise input and a group of circuits receiving independent noise. Each cluster is associated with its own local gamma generator, so all its circuits receive gamma-band input in the same phase. We find that gamma-band input differentially stabilizes the activity of the "common-noise" groups compared to the "independent-noise" groups. If the inter-cluster connections are fast, this effect is more pronounced when the gamma-band input is delivered to the clusters in the same phase rather than in the anti-phase. Assuming that the common noise comes from a large-scale distributed WM representation, our results demonstrate that local gamma oscillations can stabilize the activity of the corresponding parts of this representation, with stronger effect for fast long-range connections and synchronized gamma oscillations.
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Affiliation(s)
- Nikita Novikov
- Centre for Cognition and Decision Making, HSE University, Moscow, Russia
| | - Denis Zakharov
- Centre for Cognition and Decision Making, HSE University, Moscow, Russia
| | - Victoria Moiseeva
- Centre for Cognition and Decision Making, HSE University, Moscow, Russia
| | - Boris Gutkin
- Centre for Cognition and Decision Making, HSE University, Moscow, Russia.,Group for Neural Theory, LNC2 INSERM U960, Départment d'Études Cognitives, École Normale Supérieure, PSL Research Université, Paris, France
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21
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Kuehn C, Bick C. A universal route to explosive phenomena. SCIENCE ADVANCES 2021; 7:7/16/eabe3824. [PMID: 33863722 PMCID: PMC8051866 DOI: 10.1126/sciadv.abe3824] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/18/2020] [Accepted: 02/25/2021] [Indexed: 06/12/2023]
Abstract
Critical transitions are observed in many complex systems. This includes the onset of synchronization in a network of coupled oscillators or the emergence of an epidemic state within a population. "Explosive" first-order transitions have caught particular attention in a variety of systems when classical models are generalized by incorporating additional effects. Here, we give a mathematical argument that the emergence of these first-order transitions is not surprising but rather a universally expected effect: Varying a classical model along a generic two-parameter family must lead to a change of the criticality. To illustrate our framework, we give three explicit examples of the effect in distinct physical systems: a model of adaptive epidemic dynamics, for a generalization of the Kuramoto model, and for a percolation transition.
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Affiliation(s)
- Christian Kuehn
- Faculty of Mathematics, Technical University of Munich, Garching, Germany
- Complexity Science Hub Vienna, Vienna, Austria
| | - Christian Bick
- Department of Mathematics, University of Exeter, Exeter, UK.
- Department of Mathematics, Vrije Universiteit Amsterdam, Amsterdam, Netherlands
- Institute for Advanced Study, Technical University of Munich, Garching, Germany
- Mathematical Institute, University of Oxford, Oxford, UK
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22
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Ye W. Dynamics of a Large-Scale Spiking Neural Network with Quadratic Integrate-and-Fire Neurons. Neural Plast 2021; 2021:6623926. [PMID: 33679968 PMCID: PMC7925051 DOI: 10.1155/2021/6623926] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2020] [Revised: 01/18/2021] [Accepted: 02/05/2021] [Indexed: 11/17/2022] Open
Abstract
Since the high dimension and complexity of the large-scale spiking neural network, it is difficult to research the network dynamics. In recent decades, the mean-field approximation has been a useful method to reduce the dimension of the network. In this study, we construct a large-scale spiking neural network with quadratic integrate-and-fire neurons and reduce it to a mean-field model to research the network dynamics. We find that the activity of the mean-field model is consistent with the network activity. Based on this agreement, a two-parameter bifurcation analysis is performed on the mean-field model to understand the network dynamics. The bifurcation scenario indicates that the network model has the quiescence state, the steady state with a relatively high firing rate, and the synchronization state which correspond to the stable node, stable focus, and stable limit cycle of the system, respectively. There exist several stable limit cycles with different periods, so we can observe the synchronization states with different periods. Additionally, the model shows bistability in some regions of the bifurcation diagram which suggests that two different activities coexist in the network. The mechanisms that how these states switch are also indicated by the bifurcation curves.
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Affiliation(s)
- Weijie Ye
- School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou 510320, China
- Big data and Educational Statistics Application Laboratory, Guangdong University of Finance and Economics, Guangzhou 510320, China
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23
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Jüttner B, Henriksen C, Martens EA. Birth and destruction of collective oscillations in a network of two populations of coupled type 1 neurons. CHAOS (WOODBURY, N.Y.) 2021; 31:023141. [PMID: 33653075 DOI: 10.1063/5.0031630] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/02/2020] [Accepted: 01/12/2021] [Indexed: 06/12/2023]
Abstract
We study the macroscopic dynamics of large networks of excitable type 1 neurons composed of two populations interacting with disparate but symmetric intra- and inter-population coupling strengths. This nonuniform coupling scheme facilitates symmetric equilibria, where both populations display identical firing activity, characterized by either quiescent or spiking behavior, or asymmetric equilibria, where the firing activity of one population exhibits quiescent but the other exhibits spiking behavior. Oscillations in the firing rate are possible if neurons emit pulses with non-zero width but are otherwise quenched. Here, we explore how collective oscillations emerge for two statistically identical neuron populations in the limit of an infinite number of neurons. A detailed analysis reveals how collective oscillations are born and destroyed in various bifurcation scenarios and how they are organized around higher codimension bifurcation points. Since both symmetric and asymmetric equilibria display bistable behavior, a large configuration space with steady and oscillatory behavior is available. Switching between configurations of neural activity is relevant in functional processes such as working memory and the onset of collective oscillations in motor control.
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Affiliation(s)
- Benjamin Jüttner
- Department of Applied Mathematics and Computer Science, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark
| | - Christian Henriksen
- Department of Applied Mathematics and Computer Science, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark
| | - Erik A Martens
- Department of Applied Mathematics and Computer Science, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark
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24
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Sullivan CRP, Olsen S, Widge AS. Deep brain stimulation for psychiatric disorders: From focal brain targets to cognitive networks. Neuroimage 2021; 225:117515. [PMID: 33137473 PMCID: PMC7802517 DOI: 10.1016/j.neuroimage.2020.117515] [Citation(s) in RCA: 42] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2020] [Revised: 08/19/2020] [Accepted: 10/24/2020] [Indexed: 01/16/2023] Open
Abstract
Deep brain stimulation (DBS) is a promising intervention for treatment-resistant psychiatric disorders, particularly major depressive disorder (MDD) and obsessive-compulsive disorder (OCD). Up to 90% of patients who have not recovered with therapy or medication have reported benefit from DBS in open-label studies. Response rates in randomized controlled trials (RCTs), however, have been much lower. This has been argued to arise from surgical variability between sites, and recent psychiatric DBS research has focused on refining targeting through personalized imaging. Much less attention has been given to the fact that psychiatric disorders arise from dysfunction in distributed brain networks, and that DBS likely acts by altering communication within those networks. This is in part because psychiatric DBS research relies on subjective rating scales that make it difficult to identify network biomarkers. Here, we overview recent DBS RCT results in OCD and MDD, as well as the follow-on imaging studies. We present evidence for a new approach to studying DBS' mechanisms of action, focused on measuring objective cognitive/emotional deficits that underpin these and many other mental disorders. Further, we suggest that a focus on cognition could lead to reliable network biomarkers at an electrophysiologic level, especially those related to inter-regional synchrony of the local field potential (LFP). Developing the network neuroscience of DBS has the potential to finally unlock the potential of this highly specific therapy.
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Affiliation(s)
- Christi R P Sullivan
- University of Minnesota Medical School Department of Psychiatry and Behavioral Sciences, 2001 6th Street SE, Minneapolis, MN 55454, USA.
| | - Sarah Olsen
- University of Minnesota Medical School Department of Psychiatry and Behavioral Sciences, 2001 6th Street SE, Minneapolis, MN 55454, USA.
| | - Alik S Widge
- University of Minnesota Medical School Department of Psychiatry and Behavioral Sciences, 2001 6th Street SE, Minneapolis, MN 55454, USA.
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25
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Exact neural mass model for synaptic-based working memory. PLoS Comput Biol 2020; 16:e1008533. [PMID: 33320855 PMCID: PMC7771880 DOI: 10.1371/journal.pcbi.1008533] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/26/2020] [Revised: 12/29/2020] [Accepted: 11/12/2020] [Indexed: 01/29/2023] Open
Abstract
A synaptic theory of Working Memory (WM) has been developed in the last decade as a possible alternative to the persistent spiking paradigm. In this context, we have developed a neural mass model able to reproduce exactly the dynamics of heterogeneous spiking neural networks encompassing realistic cellular mechanisms for short-term synaptic plasticity. This population model reproduces the macroscopic dynamics of the network in terms of the firing rate and the mean membrane potential. The latter quantity allows us to gain insight of the Local Field Potential and electroencephalographic signals measured during WM tasks to characterize the brain activity. More specifically synaptic facilitation and depression integrate each other to efficiently mimic WM operations via either synaptic reactivation or persistent activity. Memory access and loading are related to stimulus-locked transient oscillations followed by a steady-state activity in the β-γ band, thus resembling what is observed in the cortex during vibrotactile stimuli in humans and object recognition in monkeys. Memory juggling and competition emerge already by loading only two items. However more items can be stored in WM by considering neural architectures composed of multiple excitatory populations and a common inhibitory pool. Memory capacity depends strongly on the presentation rate of the items and it maximizes for an optimal frequency range. In particular we provide an analytic expression for the maximal memory capacity. Furthermore, the mean membrane potential turns out to be a suitable proxy to measure the memory load, analogously to event driven potentials in experiments on humans. Finally we show that the γ power increases with the number of loaded items, as reported in many experiments, while θ and β power reveal non monotonic behaviours. In particular, β and γ rhythms are crucially sustained by the inhibitory activity, while the θ rhythm is controlled by excitatory synapses. Working Memory (WM) is the ability to temporarily store and manipulate stimuli representations that are no longer available to the senses. We have developed an innovative coarse-grained population model able to mimic several operations associated to WM. The novelty of the model consists in reproducing exactly the dynamics of spiking neural networks with realistic synaptic plasticity composed of hundreds of thousands of neurons in terms of a few macroscopic variables. These variables give access to experimentally measurable quantities such as local field potentials and electroencephalographic signals. Memory operations are joined to sustained or transient oscillations emerging in different frequency bands, in accordance with experimental results for primate and humans performing WM tasks. We have designed an architecture composed of many excitatory populations and a common inhibitory pool able to store and retain several memory items. The capacity of our multi-item architecture is around 3–5 items, a value similar to the WM capacities measured in many experiments. Furthermore, the maximal capacity is achievable only for presentation rates within an optimal frequency range. Finally, we have defined a measure of the memory load analogous to the event-related potentials employed to test humans’ WM capacity during visual memory tasks.
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26
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Montbrió E, Pazó D. Exact Mean-Field Theory Explains the Dual Role of Electrical Synapses in Collective Synchronization. PHYSICAL REVIEW LETTERS 2020; 125:248101. [PMID: 33412049 DOI: 10.1103/physrevlett.125.248101] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2020] [Revised: 11/18/2020] [Accepted: 11/18/2020] [Indexed: 06/12/2023]
Abstract
Electrical synapses play a major role in setting up neuronal synchronization, but the precise mechanisms whereby these synapses contribute to synchrony are subtle and remain elusive. To investigate these mechanisms mean-field theories for quadratic integrate-and-fire neurons with electrical synapses have been recently put forward. Still, the validity of these theories is controversial since they assume that the neurons produce unrealistic, symmetric spikes, ignoring the well-known impact of spike shape on synchronization. Here, we show that the assumption of symmetric spikes can be relaxed in such theories. The resulting mean-field equations reveal a dual role of electrical synapses: First, they equalize membrane potentials favoring the emergence of synchrony. Second, electrical synapses act as "virtual chemical synapses," which can be either excitatory or inhibitory depending upon the spike shape. Our results offer a precise mathematical explanation of the intricate effect of electrical synapses in collective synchronization. This reconciles previous theoretical and numerical works, and confirms the suitability of recent low-dimensional mean-field theories to investigate electrically coupled neuronal networks.
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Affiliation(s)
- Ernest Montbrió
- Department of Information and Communication Technologies, Universitat Pompeu Fabra, 08003 Barcelona, Spain
| | - Diego Pazó
- Instituto de Física de Cantabria (IFCA), CSIC-Universidad de Cantabria, 39005 Santander, Spain
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27
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Abstract
In this paper, inertial neural networks are under investigation, that is, the second order differential equations. The recently introduced new type of motions, unpredictable oscillations, are considered for the models. The motions continue a line of periodic and almost periodic oscillations. The research is of very strong importance for neuroscience, since the existence of unpredictable solutions proves Poincaré chaos. Sufficient conditions have been determined for the existence, uniqueness, and exponential stability of unpredictable solutions. The results can significantly extend the role of oscillations for artificial neural networks exploitation, since they provide strong new theoretical and practical opportunities for implementation of methods of chaos extension, synchronization, stabilization, and control of periodic motions in various types of neural networks. Numerical simulations are presented to demonstrate the validity of the theoretical results.
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28
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Abstract
In this paper, unpredictable oscillations in Hopfield-type neural networks is under investigation. The motion strongly relates to Poincaré chaos. Thus, the importance of the dynamics is indisputable for those problems of artificial intelligence, brain activity and robotics, which rely on chaos. Sufficient conditions for the existence and uniqueness of exponentially stable unpredictable solutions are determined. The oscillations continue the line of periodic and almost periodic motions, which already are verified as effective instruments of analysis and applications for image recognition, information processing and other areas of neuroscience. The concept of strongly unpredictable oscillations is a significant novelty of the present research, since the presence of chaos in each coordinate of the space state provides new opportunities in applications. Additionally to the theoretical analysis, we have provided strong simulation arguments, considering that all of the assumed conditions are fulfilled.
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Tal I, Neymotin S, Bickel S, Lakatos P, Schroeder CE. Oscillatory Bursting as a Mechanism for Temporal Coupling and Information Coding. Front Comput Neurosci 2020; 14:82. [PMID: 33071765 PMCID: PMC7533591 DOI: 10.3389/fncom.2020.00082] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2020] [Accepted: 07/31/2020] [Indexed: 12/03/2022] Open
Abstract
Even the simplest cognitive processes involve interactions between cortical regions. To study these processes, we usually rely on averaging across several repetitions of a task or across long segments of data to reach a statistically valid conclusion. Neuronal oscillations reflect synchronized excitability fluctuations in ensembles of neurons and can be observed in electrophysiological recordings in the presence or absence of an external stimulus. Oscillatory brain activity has been viewed as sustained increase in power at specific frequency bands. However, this perspective has been challenged in recent years by the notion that oscillations may occur as transient burst-like events that occur in individual trials and may only appear as sustained activity when multiple trials are averaged together. In this review, we examine the idea that oscillatory activity can manifest as a transient burst as well as a sustained increase in power. We discuss the technical challenges involved in the detection and characterization of transient events at the single trial level, the mechanisms that might generate them and the features that can be extracted from these events to study single-trial dynamics of neuronal ensemble activity.
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Affiliation(s)
- Idan Tal
- Department of Psychiatry, Columbia University Medical Center, New York, NY, United States.,Translational Neuroscience Division, Center for Biomedical Imaging and Neuromodulation, Nathan Kline Institute for Psychiatric Research, New York, NY, United States
| | - Samuel Neymotin
- Translational Neuroscience Division, Center for Biomedical Imaging and Neuromodulation, Nathan Kline Institute for Psychiatric Research, New York, NY, United States
| | - Stephan Bickel
- Translational Neuroscience Division, Center for Biomedical Imaging and Neuromodulation, Nathan Kline Institute for Psychiatric Research, New York, NY, United States.,Feinstein Institutes for Medical Research, Northwell Health, New York, NY, United States.,Departments of Neurosurgery and Neurology, Northwell Health, New York, NY, United States
| | - Peter Lakatos
- Translational Neuroscience Division, Center for Biomedical Imaging and Neuromodulation, Nathan Kline Institute for Psychiatric Research, New York, NY, United States.,Department of Psychiatry, New York University School of Medicine, New York, NY, United States
| | - Charles E Schroeder
- Department of Psychiatry, Columbia University Medical Center, New York, NY, United States.,Translational Neuroscience Division, Center for Biomedical Imaging and Neuromodulation, Nathan Kline Institute for Psychiatric Research, New York, NY, United States
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30
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Yamakou ME, Hjorth PG, Martens EA. Optimal Self-Induced Stochastic Resonance in Multiplex Neural Networks: Electrical vs. Chemical Synapses. Front Comput Neurosci 2020; 14:62. [PMID: 32848683 PMCID: PMC7427607 DOI: 10.3389/fncom.2020.00062] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2020] [Accepted: 05/28/2020] [Indexed: 01/23/2023] Open
Abstract
Electrical and chemical synapses shape the dynamics of neural networks, and their functional roles in information processing have been a longstanding question in neurobiology. In this paper, we investigate the role of synapses on the optimization of the phenomenon of self-induced stochastic resonance in a delayed multiplex neural network by using analytical and numerical methods. We consider a two-layer multiplex network in which, at the intra-layer level, neurons are coupled either by electrical synapses or by inhibitory chemical synapses. For each isolated layer, computations indicate that weaker electrical and chemical synaptic couplings are better optimizers of self-induced stochastic resonance. In addition, regardless of the synaptic strengths, shorter electrical synaptic delays are found to be better optimizers of the phenomenon than shorter chemical synaptic delays, while longer chemical synaptic delays are better optimizers than longer electrical synaptic delays; in both cases, the poorer optimizers are, in fact, worst. It is found that electrical, inhibitory, or excitatory chemical multiplexing of the two layers having only electrical synapses at the intra-layer levels can each optimize the phenomenon. Additionally, only excitatory chemical multiplexing of the two layers having only inhibitory chemical synapses at the intra-layer levels can optimize the phenomenon. These results may guide experiments aimed at establishing or confirming to the mechanism of self-induced stochastic resonance in networks of artificial neural circuits as well as in real biological neural networks.
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Affiliation(s)
- Marius E. Yamakou
- Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig, Germany
- Department of Applied Mathematics and Computer Science, Technical University of Denmark, Lyngby, Denmark
| | - Poul G. Hjorth
- Department of Applied Mathematics and Computer Science, Technical University of Denmark, Lyngby, Denmark
| | - Erik A. Martens
- Department of Applied Mathematics and Computer Science, Technical University of Denmark, Lyngby, Denmark
- Department of Biomedical Science, University of Copenhagen, Copenhagen, Denmark
- Centre for Translational Neuromedicine, University of Copenhagen, Copenhagen, Denmark
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31
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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: 17] [Impact Index Per Article: 4.3] [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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32
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Bick C, Goodfellow M, Laing CR, Martens EA. Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review. JOURNAL OF MATHEMATICAL NEUROSCIENCE 2020; 10:9. [PMID: 32462281 PMCID: PMC7253574 DOI: 10.1186/s13408-020-00086-9] [Citation(s) in RCA: 93] [Impact Index Per Article: 23.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2019] [Accepted: 05/07/2020] [Indexed: 05/03/2023]
Abstract
Many biological and neural systems can be seen as networks of interacting periodic processes. Importantly, their functionality, i.e., whether these networks can perform their function or not, depends on the emerging collective dynamics of the network. Synchrony of oscillations is one of the most prominent examples of such collective behavior and has been associated both with function and dysfunction. Understanding how network structure and interactions, as well as the microscopic properties of individual units, shape the emerging collective dynamics is critical to find factors that lead to malfunction. However, many biological systems such as the brain consist of a large number of dynamical units. Hence, their analysis has either relied on simplified heuristic models on a coarse scale, or the analysis comes at a huge computational cost. Here we review recently introduced approaches, known as the Ott-Antonsen and Watanabe-Strogatz reductions, allowing one to simplify the analysis by bridging small and large scales. Thus, reduced model equations are obtained that exactly describe the collective dynamics for each subpopulation in the oscillator network via few collective variables only. The resulting equations are next-generation models: Rather than being heuristic, they exactly link microscopic and macroscopic descriptions and therefore accurately capture microscopic properties of the underlying system. At the same time, they are sufficiently simple to analyze without great computational effort. In the last decade, these reduction methods have become instrumental in understanding how network structure and interactions shape the collective dynamics and the emergence of synchrony. We review this progress based on concrete examples and outline possible limitations. Finally, we discuss how linking the reduced models with experimental data can guide the way towards the development of new treatment approaches, for example, for neurological disease.
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Affiliation(s)
- Christian Bick
- Centre for Systems, Dynamics, and Control, University of Exeter, Exeter, UK.
- Department of Mathematics, University of Exeter, Exeter, UK.
- EPSRC Centre for Predictive Modelling in Healthcare, University of Exeter, Exeter, UK.
- Mathematical Institute, University of Oxford, Oxford, UK.
- Institute for Advanced Study, Technische Universität München, Garching, Germany.
| | - Marc Goodfellow
- Department of Mathematics, University of Exeter, Exeter, UK
- EPSRC Centre for Predictive Modelling in Healthcare, University of Exeter, Exeter, UK
- Living Systems Institute, University of Exeter, Exeter, UK
- Wellcome Trust Centre for Biomedical Modelling and Analysis, University of Exeter, Exeter, UK
| | - Carlo R Laing
- School of Natural and Computational Sciences, Massey University, Auckland, New Zealand
| | - Erik A Martens
- Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kgs. Lyngby, Denmark.
- Department of Biomedical Science, University of Copenhagen, Copenhagen N, Denmark.
- Centre for Translational Neuroscience, University of Copenhagen, Copenhagen N, Denmark.
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33
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Pietras B, Devalle F, Roxin A, Daffertshofer A, Montbrió E. Exact firing rate model reveals the differential effects of chemical versus electrical synapses in spiking networks. Phys Rev E 2020; 100:042412. [PMID: 31771022 DOI: 10.1103/physreve.100.042412] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2019] [Indexed: 01/09/2023]
Abstract
Chemical and electrical synapses shape the dynamics of neuronal networks. Numerous theoretical studies have investigated how each of these types of synapses contributes to the generation of neuronal oscillations, but their combined effect is less understood. This limitation is further magnified by the impossibility of traditional neuronal mean-field models-also known as firing rate models or firing rate equations-to account for electrical synapses. Here, we introduce a firing rate model that exactly describes the mean-field dynamics of heterogeneous populations of quadratic integrate-and-fire (QIF) neurons with both chemical and electrical synapses. The mathematical analysis of the firing rate model reveals a well-established bifurcation scenario for networks with chemical synapses, characterized by a codimension-2 cusp point and persistent states for strong recurrent excitatory coupling. The inclusion of electrical coupling generally implies neuronal synchrony by virtue of a supercritical Hopf bifurcation. This transforms the cusp scenario into a bifurcation scenario characterized by three codimension-2 points (cusp, Takens-Bogdanov, and saddle-node separatrix loop), which greatly reduces the possibility for persistent states. This is generic for heterogeneous QIF networks with both chemical and electrical couplings. Our results agree with several numerical studies on the dynamics of large networks of heterogeneous spiking neurons with electrical and chemical couplings.
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Affiliation(s)
- Bastian Pietras
- Faculty of Behavioural and Movement Sciences, Amsterdam Movement Sciences & Institute of Brain and Behavior Amsterdam, Vrije Universiteit Amsterdam, van der Boechorststraat 9, Amsterdam 1081 BT, The Netherlands.,Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom.,Institute of Mathematics, Technical University Berlin, 10623 Berlin, Germany.,Bernstein Center for Computational Neuroscience Berlin, 10115 Berlin, Germany
| | - Federico Devalle
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom.,Department of Information and Communication Technologies, Universitat Pompeu Fabra, 08003 Barcelona, Spain
| | - Alex Roxin
- Centre de Recerca Matemàtica, Campus de Bellaterra, Edifici C, 08193 Bellaterra (Barcelona), Spain.,Barcelona Graduate School of Mathematics, 08193 Barcelona, Spain
| | - Andreas Daffertshofer
- Faculty of Behavioural and Movement Sciences, Amsterdam Movement Sciences & Institute of Brain and Behavior Amsterdam, Vrije Universiteit Amsterdam, van der Boechorststraat 9, Amsterdam 1081 BT, The Netherlands
| | - Ernest Montbrió
- Department of Information and Communication Technologies, Universitat Pompeu Fabra, 08003 Barcelona, Spain
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34
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Schmidt H, Avitabile D. Bumps and oscillons in networks of spiking neurons. CHAOS (WOODBURY, N.Y.) 2020; 30:033133. [PMID: 32237760 DOI: 10.1063/1.5135579] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/06/2019] [Accepted: 03/03/2020] [Indexed: 06/11/2023]
Abstract
We study localized patterns in an exact mean-field description of a spatially extended network of quadratic integrate-and-fire neurons. We investigate conditions for the existence and stability of localized solutions, so-called bumps, and give an analytic estimate for the parameter range, where these solutions exist in parameter space, when one or more microscopic network parameters are varied. We develop Galerkin methods for the model equations, which enable numerical bifurcation analysis of stationary and time-periodic spatially extended solutions. We study the emergence of patterns composed of multiple bumps, which are arranged in a snake-and-ladder bifurcation structure if a homogeneous or heterogeneous synaptic kernel is suitably chosen. Furthermore, we examine time-periodic, spatially localized solutions (oscillons) in the presence of external forcing, and in autonomous, recurrently coupled excitatory and inhibitory networks. In both cases, we observe period-doubling cascades leading to chaotic oscillations.
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Affiliation(s)
- Helmut Schmidt
- Max Planck Institute for Human Cognitive and Brain Sciences, Stephanstrasse 1a, 04103 Leipzig, Germany
| | - Daniele Avitabile
- Department of Mathematics, Faculteit der Exacte Wetenschappen, Vrije Universiteit (VU University Amsterdam), De Boelelaan 1081a, 1081 HV Amsterdam, Netherlands and Mathneuro Team, Inria Sophia Antipolis, 2004 Rue des Lucioles, Sophia Antipolis, 06902 Cedex, France
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35
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Schwalger T, Chizhov AV. Mind the last spike - firing rate models for mesoscopic populations of spiking neurons. Curr Opin Neurobiol 2019; 58:155-166. [PMID: 31590003 DOI: 10.1016/j.conb.2019.08.003] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2019] [Accepted: 08/25/2019] [Indexed: 02/07/2023]
Abstract
The dominant modeling framework for understanding cortical computations are heuristic firing rate models. Despite their success, these models fall short to capture spike synchronization effects, to link to biophysical parameters and to describe finite-size fluctuations. In this opinion article, we propose that the refractory density method (RDM), also known as age-structured population dynamics or quasi-renewal theory, yields a powerful theoretical framework to build rate-based models for mesoscopic neural populations from realistic neuron dynamics at the microscopic level. We review recent advances achieved by the RDM to obtain efficient population density equations for networks of generalized integrate-and-fire (GIF) neurons - a class of neuron models that has been successfully fitted to various cell types. The theory not only predicts the nonstationary dynamics of large populations of neurons but also permits an extension to finite-size populations and a systematic reduction to low-dimensional rate dynamics. The new types of rate models will allow a re-examination of models of cortical computations under biological constraints.
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Affiliation(s)
- Tilo Schwalger
- Bernstein Center for Computational Neuroscience, 10115 Berlin, Germany; Institut für Mathematik, Technische Universität Berlin, 10623 Berlin, Germany.
| | - Anton V Chizhov
- Ioffe Institute, 194021 Saint-Petersburg, Russia; Sechenov Institute of Evolutionary Physiology and Biochemistry of the Russian Academy of Sciences, 194223 Saint-Petersburg, Russia
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36
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Seleznov I, Zyma I, Kiyono K, Tukaev S, Popov A, Chernykh M, Shpenkov O. Detrended Fluctuation, Coherence, and Spectral Power Analysis of Activation Rearrangement in EEG Dynamics During Cognitive Workload. Front Hum Neurosci 2019; 13:270. [PMID: 31440151 PMCID: PMC6694837 DOI: 10.3389/fnhum.2019.00270] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2019] [Accepted: 07/19/2019] [Indexed: 12/31/2022] Open
Abstract
In the study of human cognitive activity using electroencephalogram (EEG), the brain dynamics parameters and characteristics play a crucial role. They allow to investigate the changes in functionality depending on the environment and task performance process, and also to access the intensity of the brain activity in various locations of the cortex and its dependencies. Usually, the dynamics of activation of different brain areas during the cognitive tasks are being studied by spectral analysis based on power spectral density (PSD) estimation, and coherence analysis, which are de facto standard tools in quantitative characterization of brain activity. PSD and coherence reflect the strength of oscillations and similarity of the emergence of these oscillations in the brain, respectively, while the concept of stability of brain activity over time is not well defined and less formalized. We propose to employ the detrended fluctuation analysis (DFA) as a measure of the EEG persistence over time, and use the DFA scaling exponent as its quantitative characteristics. We applied DFA to the study of the changes in activation in brain dynamics during mental calculations and united it with PSD and coherence estimation. In the experiment, EEGs during resting state and mental serial subtraction from 36 subjects were recorded and analyzed in four frequency ranges: θ1 (4.1-5.8 Hz), θ2 (5.9-7.4 Hz), β1 (13-19.9 Hz), and β2 (20-25 Hz). PSD maps to access the intensity of cortex activation and coherence to quantify the connections between different brain areas were calculated, the distribution of DFA scaling exponent over the head surface was exploited to measure the time characteristics of the dynamics of brain activity. Obtained arrangements of DFA scaling exponent suggest that normal functioning of the brain is characterized by long-term temporal correlations in the cortex. Topographical distribution of the DFA scaling exponent was comparable for θ and β frequency bands, demonstrating the largest values of DFA scaling exponent during cognitive activation. The study shows that the long-term temporal correlations evaluated by DFA can be of great interest for diagnosis of the variety of brain dysfunctions of different etiology in the future.
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Affiliation(s)
- Ivan Seleznov
- Department of Electronic Engineering, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine
| | - Igor Zyma
- Department of Physiology and Anatomy, Educational and Scientific Center “Institute of Biology and Medicine”, National Taras Shevchenko University of Kyiv, Kyiv, Ukraine
| | - Ken Kiyono
- Division of Bioengineering, Graduate School of Engineering Science, Osaka University, Osaka, Japan
| | - Sergii Tukaev
- Department of Physiology of Brain and Psychophysiology, Educational and Scientific Centre “Institute of Biology and Medicine”, National Taras Shevchenko University of Kyiv, Kyiv, Ukraine
- Department of Social Communication, Institute of Journalism, National Taras Shevchenko University of Kyiv, Kyiv, Ukraine
- Laboratory on Theory and Methodic of Sport Preparation and Reserve Capabilities of Athletes, Scientific Research Institute, National University of Physical Education and Sports of Ukraine, Kyiv, Ukraine
| | - Anton Popov
- Department of Electronic Engineering, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine
- R&D Engineering, Ciklum, London, United Kingdom
| | - Mariia Chernykh
- Department of Biophysics and Medical Informatics, Educational and Scientific Center “Institute of Biology and Medicine”, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine
| | - Oleksii Shpenkov
- Department of Physiology and Anatomy, Educational and Scientific Center “Institute of Biology and Medicine”, National Taras Shevchenko University of Kyiv, Kyiv, Ukraine
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37
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Observable for a Large System of Globally Coupled Excitable Units. MATHEMATICAL AND COMPUTATIONAL APPLICATIONS 2019. [DOI: 10.3390/mca24020037] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
The study of large arrays of coupled excitable systems has largely benefited from a technique proposed by Ott and Antonsen, which results in a low dimensional system of equations for the system’s order parameter. In this work, we show how to explicitly introduce a variable describing the global synaptic activation of the network into these family of models. This global variable is built by adding realistic synaptic time traces. We propose that this variable can, under certain conditions, be a good proxy for the local field potential of the network. We report experimental, in vivo, electrophysiology data supporting this claim.
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38
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Latzer P, Shchyglo O, Hartl T, Matschke V, Schlegel U, Manahan-Vaughan D, Theiss C. Blocking VEGF by Bevacizumab Compromises Electrophysiological and Morphological Properties of Hippocampal Neurons. Front Cell Neurosci 2019; 13:113. [PMID: 30971896 PMCID: PMC6445260 DOI: 10.3389/fncel.2019.00113] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2018] [Accepted: 03/07/2019] [Indexed: 12/20/2022] Open
Abstract
A hallmark of glioblastoma multiforme (GBM) is neoangiogenesis, mediated by the overexpression of vascular endothelial growth factor (VEGF). Anti-VEGF antibodies, like bevacizumab, prolong progression-free survival in GBM, however, this treatment has been reported to be associated with a decline in neurocognitive function. Therefore, this study focused on the effects of bevacizumab on neuronal function and plasticity. We analyzed neuronal membrane properties and synaptic plasticity in rat hippocampal slices, as well as spine dynamics in dissociated hippocampal neurons, to examine the impact of bevacizumab on hippocampal function and viability. VEGF inhibition resulted in profound impairments in hippocampal synaptic plasticity as well as reductions in dendritic spine number and length. Physiological properties of hippocampal neurons were also affected. These effects of VEGF blockade on hippocampal function may play a role in compromising memory and information processing and thus, may contribute to neurocognitive dysfunction in GBM patients treated with bevacizumab.
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Affiliation(s)
- Pauline Latzer
- Department of Cytology, Institute of Anatomy, Ruhr University Bochum, Bochum, Germany.,International Graduate School of Neuroscience, Ruhr University Bochum, Bochum, Germany
| | - Olena Shchyglo
- Department of Neurophysiology, Medical Faculty, Ruhr University Bochum, Bochum, Germany
| | - Tim Hartl
- International Graduate School of Neuroscience, Ruhr University Bochum, Bochum, Germany.,Department of Neurophysiology, Medical Faculty, Ruhr University Bochum, Bochum, Germany
| | - Veronika Matschke
- Department of Cytology, Institute of Anatomy, Ruhr University Bochum, Bochum, Germany
| | - Uwe Schlegel
- Department of Neurology, Knappschaftskrankenhaus, Ruhr University Bochum, Bochum, Germany
| | | | - Carsten Theiss
- Department of Cytology, Institute of Anatomy, Ruhr University Bochum, Bochum, Germany
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39
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Reaction Time Improvements by Neural Bistability. Behav Sci (Basel) 2019; 9:bs9030028. [PMID: 30889937 PMCID: PMC6466602 DOI: 10.3390/bs9030028] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2018] [Revised: 01/22/2019] [Accepted: 03/12/2019] [Indexed: 12/16/2022] Open
Abstract
The often reported reduction of Reaction Time (RT) by Vision Training) is successfully replicated by 81 athletes across sports. This enabled us to achieve a mean reduction of RTs for athletes eye-hand coordination of more than 10%, with high statistical significance. We explain how such an observed effect of Sensorimotor systems' plasticity causing reduced RT can last in practice for multiple days and even weeks in subjects, via a proof of principle. Its mathematical neural model can be forced outside a previous stable (but long) RT into a state leading to reduced eye-hand coordination RT, which is, again, in a stable neural state.
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