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Parastesh F, Rajagopal K, Jafari S, Perc M, Schöll E. Blinking coupling enhances network synchronization. Phys Rev E 2022; 105:054304. [PMID: 35706266 DOI: 10.1103/physreve.105.054304] [Citation(s) in RCA: 19] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2021] [Accepted: 04/13/2022] [Indexed: 06/15/2023]
Abstract
This paper studies the synchronization of a network with linear diffusive coupling, which blinks between the variables periodically. The synchronization of the blinking network in the case of sufficiently fast blinking is analyzed by showing that the stability of the synchronous solution depends only on the averaged coupling and not on the instantaneous coupling. To illustrate the effect of the blinking period on the network synchronization, the Hindmarsh-Rose model is used as the dynamics of nodes. The synchronization is investigated by considering constant single-variable coupling, averaged coupling, and blinking coupling through a linear stability analysis. It is observed that by decreasing the blinking period, the required coupling strength for synchrony is reduced. It equals that of the averaged coupling model times the number of variables. However, in the averaged coupling, all variables participate in the coupling, while in the blinking model only one variable is coupled at any time. Therefore, the blinking coupling leads to an enhanced synchronization in comparison with the single-variable coupling. Numerical simulations of the average synchronization error of the network confirm the results obtained from the linear stability analysis.
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Affiliation(s)
- Fatemeh Parastesh
- Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Iran
| | | | - Sajad Jafari
- Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Iran
- Health Technology Research Institute, Amirkabir University of Technology (Tehran Polytechnic), Iran
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška Cesta 160, 2000 Maribor, Slovenia
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 404332, Taiwan
- Complexity Science Hub Vienna, Josefstädterstraße 39, 1080 Vienna, Austria
| | - Eckehard Schöll
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, D-10623 Berlin, Germany
- Bernstein Center for Computational Neuroscience Berlin, Humboldt-Universität, D-10115 Berlin, Germany
- Potsdam Institute for Climate Impact Research, Telegrafenberg A 31, D-14473 Potsdam, Germany
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Hattori K, Hayakawa T, Nakanishi A, Ishida M, Yamamoto H, Hirano-Iwata A, Tanii T. Contribution of AMPA and NMDA receptors in the spontaneous firing patterns of single neurons in autaptic culture. Biosystems 2020; 198:104278. [PMID: 33075473 DOI: 10.1016/j.biosystems.2020.104278] [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: 03/29/2020] [Revised: 10/11/2020] [Accepted: 10/14/2020] [Indexed: 10/23/2022]
Abstract
Single neurons in an autaptic culture exhibit various types of firing pattern with different firing durations and rhythms. However, a neuron with autapses has often been modeled as an oscillator providing a monotonic firing pattern with a constant periodicity because of the lack of a mathematical model. In the work described in this study, we use computational simulation and whole-cell patch-clamp recording to elucidate and model the mechanism by which such neurons generate various firing pattens. In the computational simulation, three types of spontaneous firing pattern, i.e., short, long-lasting, and periodic burst firing patterns are realized by changing the combination ratio of N-methyl-d-aspartate (NMDA) to α-amino-3-hydroxyl-5-methyl-4-isoxazole-propionate (AMPA) conductance. These three types of firing patterns are also observed in the experiments where neurons are cultured in isolation on micropatterned substrates. Using the AMPA and NMDA current models, we discuss that, in principle, autapses can regulate rhythmicity and information selection in neuronal networks.
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Affiliation(s)
- Kouhei Hattori
- Waseda University, Faculty of Science and Engineering, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555, Japan.
| | - Takeshi Hayakawa
- Tohoku University, Research Institute of Electrical Communication, 2-1-1 Katahira, Aoba, Sendai 980-8577, Japan
| | - Akira Nakanishi
- Waseda University, Faculty of Science and Engineering, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555, Japan
| | - Mihoko Ishida
- Waseda University, Faculty of Science and Engineering, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555, Japan
| | - Hideaki Yamamoto
- Tohoku University, Research Institute of Electrical Communication, 2-1-1 Katahira, Aoba, Sendai 980-8577, Japan
| | - Ayumi Hirano-Iwata
- Tohoku University, Research Institute of Electrical Communication, 2-1-1 Katahira, Aoba, Sendai 980-8577, Japan; Tohoku University, WPI-Advanced Institute for Materials Research (WPI-AIMR), 2-1-1 Katahira, Aoba, Sendai 980-8577, Japan
| | - Takashi Tanii
- Waseda University, Faculty of Science and Engineering, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555, Japan
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Zhao Z, Gu H. Transitions between classes of neuronal excitability and bifurcations induced by autapse. Sci Rep 2017; 7:6760. [PMID: 28755006 PMCID: PMC5533805 DOI: 10.1038/s41598-017-07051-9] [Citation(s) in RCA: 57] [Impact Index Per Article: 8.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2017] [Accepted: 06/21/2017] [Indexed: 11/10/2022] Open
Abstract
Neuronal excitabilities behave as the basic and important dynamics related to the transitions between firing and resting states, and are characterized by distinct bifurcation types and spiking frequency responses. Switches between class I and II excitabilities induced by modulations outside the neuron (for example, modulation to M-type potassium current) have been one of the most concerning issues in both electrophysiology and nonlinear dynamics. In the present paper, we identified switches between 2 classes of excitability and firing frequency responses when an autapse, which widely exists in real nervous systems and plays important roles via self-feedback, is introduced into the Morris-Lecar (ML) model neuron. The transition from class I to class II excitability and from class II to class I spiking frequency responses were respectively induced by the inhibitory and excitatory autapse, which are characterized by changes of bifurcations, frequency responses, steady-state current-potential curves, and nullclines. Furthermore, we identified codimension-1 and -2 bifurcations and the characteristics of the current-potential curve that determine the transitions. Our results presented a comprehensive relationship between 2 classes of neuronal excitability/spiking characterized by different types of bifurcations, along with a novel possible function of autapse or self-feedback control on modulating neuronal excitability.
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Affiliation(s)
- Zhiguo Zhao
- School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092, China
| | - Huaguang Gu
- School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092, China.
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