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Přibylová L, Ševčík J, Eclerová V, Klimeš P, Brázdil M, Meijer HGE. Weak coupling of neurons enables very high-frequency and ultra-fast oscillations through the interplay of synchronized phase shifts. Netw Neurosci 2024; 8:293-318. [PMID: 38562290 PMCID: PMC10954350 DOI: 10.1162/netn_a_00351] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2023] [Accepted: 11/21/2023] [Indexed: 04/04/2024] Open
Abstract
Recently, in the past decade, high-frequency oscillations (HFOs), very high-frequency oscillations (VHFOs), and ultra-fast oscillations (UFOs) were reported in epileptic patients with drug-resistant epilepsy. However, to this day, the physiological origin of these events has yet to be understood. Our study establishes a mathematical framework based on bifurcation theory for investigating the occurrence of VHFOs and UFOs in depth EEG signals of patients with focal epilepsy, focusing on the potential role of reduced connection strength between neurons in an epileptic focus. We demonstrate that synchronization of a weakly coupled network can generate very and ultra high-frequency signals detectable by nearby microelectrodes. In particular, we show that a bistability region enables the persistence of phase-shift synchronized clusters of neurons. This phenomenon is observed for different hippocampal neuron models, including Morris-Lecar, Destexhe-Paré, and an interneuron model. The mechanism seems to be robust for small coupling, and it also persists with random noise affecting the external current. Our findings suggest that weakened neuronal connections could contribute to the production of oscillations with frequencies above 1000 Hz, which could advance our understanding of epilepsy pathology and potentially improve treatment strategies. However, further exploration of various coupling types and complex network models is needed.
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Affiliation(s)
- Lenka Přibylová
- Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Brno, Czech Republic
| | - Jan Ševčík
- Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Brno, Czech Republic
| | - Veronika Eclerová
- Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Brno, Czech Republic
| | - Petr Klimeš
- Institute of Scientific Instruments, The Czech Academy of Sciences, Brno, Czech Republic
| | - Milan Brázdil
- Brno Epilepsy Center, Dept. of Neurology, St. Anne’s Univ. Hospital and Faculty of Medicine, Masaryk University, Brno, Czech Republic, member of the ERN EpiCARE
- Behavioral and Social Neuroscience Research Group, Central European Institute of Technology, Masaryk University, Brno, Czech Republic
| | - Hil G. E. Meijer
- Department of Applied Mathematics, Techmed Centre, University of Twente, Enschede, The Netherlands
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Biswas S, Ghosh D. Evolutionarily stable strategies to overcome Allee effect in predator-prey interaction. CHAOS (WOODBURY, N.Y.) 2023; 33:2894469. [PMID: 37276555 DOI: 10.1063/5.0145914] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2023] [Accepted: 05/08/2023] [Indexed: 06/07/2023]
Abstract
Every successful species invasion is facilitated by both ecological and evolutionary mechanisms. The evolution of population's fitness related traits acts as functional adaptations to Allee effects. This trade-off increases predatory success at an expense of elevated death rate of potential predators. We address our queries employing an eco-evolutionary modeling approach that provides a means of circumventing inverse density-dependent effect. In the absence of evolution, the ecological system potentially exhibits multi-stable configurations under identical ecological conditions by allowing different bifurcation scenarios with the Allee effect. The model predicts a high risk of catastrophic extinction of interacting populations around different types of saddle-node bifurcations resulting from the increased Allee effect. We adopt the game-theoretic approach to derive the analytical conditions for the emergence of evolutionarily stable strategy (ESS) when the ecological system possesses asymptotically stable steady states as well as population cycles. We establish that ESSs occur at those values of adopted evolutionary strategies that are local optima of some functional forms of model parameters. Overall, our theoretical study provides important ecological insights in predicting successful biological invasions in the light of evolution.
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Affiliation(s)
- Saswati Biswas
- Department of Mathematics, University of Kalyani, Kalyani, Nadia 741235, India
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata 700108, India
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Sharma SK, Mondal A, Kaslik E, Hens C, Antonopoulos CG. Diverse electrical responses in a network of fractional-order conductance-based excitable Morris-Lecar systems. Sci Rep 2023; 13:8215. [PMID: 37217514 DOI: 10.1038/s41598-023-34807-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2022] [Accepted: 05/08/2023] [Indexed: 05/24/2023] Open
Abstract
The diverse excitabilities of cells often produce various spiking-bursting oscillations that are found in the neural system. We establish the ability of a fractional-order excitable neuron model with Caputo's fractional derivative to analyze the effects of its dynamics on the spike train features observed in our results. The significance of this generalization relies on a theoretical framework of the model in which memory and hereditary properties are considered. Employing the fractional exponent, we first provide information about the variations in electrical activities. We deal with the 2D class I and class II excitable Morris-Lecar (M-L) neuron models that show the alternation of spiking and bursting features including MMOs & MMBOs of an uncoupled fractional-order neuron. We then extend the study with the 3D slow-fast M-L model in the fractional domain. The considered approach establishes a way to describe various characteristics similarities between fractional-order and classical integer-order dynamics. Using the stability and bifurcation analysis, we discuss different parameter spaces where the quiescent state emerges in uncoupled neurons. We show the characteristics consistent with the analytical results. Next, the Erdös-Rényi network of desynchronized mixed neurons (oscillatory and excitable) is constructed that is coupled through membrane voltage. It can generate complex firing activities where quiescent neurons start to fire. Furthermore, we have shown that increasing coupling can create cluster synchronization, and eventually it can enable the network to fire in unison. Based on cluster synchronization, we develop a reduced-order model which can capture the activities of the entire network. Our results reveal that the effect of fractional-order depends on the synaptic connectivity and the memory trace of the system. Additionally, the dynamics captures spike frequency adaptation and spike latency that occur over multiple timescales as the effects of fractional derivative, which has been observed in neural computation.
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Affiliation(s)
- Sanjeev K Sharma
- Department of Mathematics, VIT-AP University, Amaravati, 522237, Andhra Pradesh, India
| | - Argha Mondal
- Department of Mathematics, Sidho-Kanho-Birsha University, Purulia, 723104, West Bengal, India.
- Department of Mathematical Sciences, University of Essex, Wivenhoe Park, Colchester, UK.
| | - Eva Kaslik
- Department of Mathematics and Computer Science, West University of Timisoara, Timisoara, Romania.
- Institute for Advanced Environmental Research, West University of Timisoara, Timisoara, Romania.
| | | | - Chris G Antonopoulos
- Department of Mathematical Sciences, University of Essex, Wivenhoe Park, Colchester, UK.
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Roy M, Senapati A, Poria S, Mishra A, Hens C. Role of assortativity in predicting burst synchronization using echo state network. Phys Rev E 2022; 105:064205. [PMID: 35854538 DOI: 10.1103/physreve.105.064205] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2021] [Accepted: 05/11/2022] [Indexed: 06/15/2023]
Abstract
In this study, we use a reservoir computing based echo state network (ESN) to predict the collective burst synchronization of neurons. Specifically, we investigate the ability of ESN in predicting the burst synchronization of an ensemble of Rulkov neurons placed on a scale-free network. We have shown that a limited number of nodal dynamics used as input in the machine can capture the real trend of burst synchronization in this network. Further, we investigate the proper selection of nodal inputs of degree-degree (positive and negative) correlated networks. We show that for a disassortative network, selection of different input nodes based on degree has no significant role in the machine's prediction. However, in the case of assortative network, training the machine with the information (i.e., time series) of low degree nodes gives better results in predicting the burst synchronization. The results are found to be consistent with the investigation carried out with a continuous time Hindmarsh-Rose neuron model. Furthermore, the role of hyperparameters like spectral radius and leaking parameter of ESN on the prediction process has been examined. Finally, we explain the underlying mechanism responsible for observing these differences in the prediction in a degree correlated network.
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Affiliation(s)
- Mousumi Roy
- Department of Applied Mathematics, University of Calcutta, 92, A.P.C. Road, Kolkata 700009, India
| | - Abhishek Senapati
- Center for Advanced Systems Understanding (CASUS), 02826 Görlitz, Germany
| | - Swarup Poria
- Department of Applied Mathematics, University of Calcutta, 92, A.P.C. Road, Kolkata 700009, India
| | - Arindam Mishra
- Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90924 Lodz, Poland
| | - Chittaranjan Hens
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
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Kumar Verma U, Ambika G. Emergent Dynamics and Spatio Temporal Patterns on Multiplex Neuronal Networks. Front Comput Neurosci 2021; 15:774969. [PMID: 34924985 PMCID: PMC8674435 DOI: 10.3389/fncom.2021.774969] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2021] [Accepted: 11/01/2021] [Indexed: 11/16/2022] Open
Abstract
We present a study on the emergence of a variety of spatio temporal patterns among neurons that are connected in a multiplex framework, with neurons on two layers with different functional couplings. With the Hindmarsh-Rose model for the dynamics of single neurons, we analyze the possible patterns of dynamics in each layer separately and report emergent patterns of activity like in-phase synchronized oscillations and amplitude death (AD) for excitatory coupling and anti-phase mixed-mode oscillations (MMO) in multi-clusters with phase regularities when the connections are inhibitory. When they are multiplexed, with neurons of one layer coupled with excitatory synaptic coupling and neurons of the other layer coupled with inhibitory synaptic coupling, we observe the transfer or selection of interesting patterns of collective behavior between the layers. While the revival of oscillations occurs in the layer with excitatory coupling, the transition from anti-phase to in-phase and vice versa is observed in the other layer with inhibitory synaptic coupling. We also discuss how the selection of these spatio temporal patterns can be controlled by tuning the intralayer or interlayer coupling strengths or increasing the range of non-local coupling. With one layer having electrical coupling while the other synaptic coupling of excitatory(inhibitory)type, we find in-phase(anti-phase) synchronized patterns of activity among neurons in both layers.
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Affiliation(s)
| | - G. Ambika
- Department of Physics, Indian Institute of Science Education and Research Tirupati, Tirupati, India
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Mishra A, Ghosh S, Kumar Dana S, Kapitaniak T, Hens C. Neuron-like spiking and bursting in Josephson junctions: A review. CHAOS (WOODBURY, N.Y.) 2021; 31:052101. [PMID: 34240928 DOI: 10.1063/5.0050526] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2021] [Accepted: 04/30/2021] [Indexed: 06/13/2023]
Abstract
The superconducting Josephson junction shows spiking and bursting behaviors, which have similarities with neuronal spiking and bursting. This phenomenon had been observed long ago by some researchers; however, they overlooked the biological similarity of this particular dynamical feature and never attempted to interpret it from the perspective of neuronal dynamics. In recent times, the origin of such a strange property of the superconducting junction has been explained and such neuronal functional behavior has also been observed in superconducting nanowires. The history of this research is briefly reviewed here with illustrations from studies of two junction models and their dynamical interpretation in the sense of biological bursting.
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Affiliation(s)
- Arindam Mishra
- Department of Mathematics, Jadavpur University, Kolkata 700032, India
| | - Subrata Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
| | - Syamal Kumar Dana
- Department of Mathematics, Jadavpur University, Kolkata 700032, India
| | - Tomasz Kapitaniak
- Division of Dynamics, Lodz University of Technology, 90-924 Lodz, Poland
| | - Chittaranjan Hens
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
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Sharma SK, Mondal A, Mondal A, Upadhyay RK, Hens C. Emergence of bursting in a network of memory dependent excitable and spiking leech-heart neurons. J R Soc Interface 2020; 17:20190859. [PMID: 32574543 DOI: 10.1098/rsif.2019.0859] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Abstract
Excitable cells often produce different oscillatory activities that help us to understand the transmitting and processing of signals in the neural system. The diverse excitabilities of an individual neuron can be reproduced by a fractional-order biophysical model that preserves several previous memory effects. However, it is not completely clear to what extent the fractional-order dynamics changes the firing properties of excitable cells. In this article, we investigate the alternation of spiking and bursting phenomena of an uncoupled and coupled fractional leech-heart (L-H) neurons. We show that a complete graph of heterogeneous de-synchronized neurons in the backdrop of diverse memory settings (a mixture of integer and fractional exponents) can eventually lead to bursting with the formation of cluster synchronization over a certain threshold of coupling strength, however, the uncoupled L-H neurons cannot reveal bursting dynamics. Using the stability analysis in fractional domain, we demarcate the parameter space where the quiescent or steady-state emerges in uncoupled L-H neuron. Finally, a reduced-order model is introduced to capture the activities of the large network of fractional-order model neurons.
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Affiliation(s)
- Sanjeev Kumar Sharma
- Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad 826004, India
| | - Argha Mondal
- Computational Neuroscience Center, University of Washington, Seattle, WA, USA.,Physics and Applied Mathematics Unit, Indian Statistical Institute, BT Road, Kolkata 700108, India
| | - Arnab Mondal
- Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad 826004, India
| | - Ranjit Kumar Upadhyay
- Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad 826004, India
| | - Chittaranjan Hens
- Physics and Applied Mathematics Unit, Indian Statistical Institute, BT Road, Kolkata 700108, India
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