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Scully J, Bourahmah J, Bloom D, Shilnikov AL. Pairing cellular and synaptic dynamics into building blocks of rhythmic neural circuits. A tutorial. FRONTIERS IN NETWORK PHYSIOLOGY 2024; 4:1397151. [PMID: 38983123 PMCID: PMC11231435 DOI: 10.3389/fnetp.2024.1397151] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/06/2024] [Accepted: 05/16/2024] [Indexed: 07/11/2024]
Abstract
In this study we focus on two subnetworks common in the circuitry of swim central pattern generators (CPGs) in the sea slugs, Melibe leonina and Dendronotus iris and show that they are independently capable of stably producing emergent network bursting. This observation raises the question of whether the coordination of redundant bursting mechanisms plays a role in the generation of rhythm and its regulation in the given swim CPGs. To address this question, we investigate two pairwise rhythm-generating networks and examine the properties of their fundamental components: cellular and synaptic, which are crucial for proper network assembly and its stable function. We perform a slow-fast decomposition analysis of cellular dynamics and highlight its significant bifurcations occurring in isolated and coupled neurons. A novel model for slow synapses with high filtering efficiency and temporal delay is also introduced and examined. Our findings demonstrate the existence of two modes of oscillation in bicellular rhythm-generating networks with network hysteresis: i) a half-center oscillator and ii) an excitatory-inhibitory pair. These 2-cell networks offer potential as common building blocks combined in modular organization of larger neural circuits preserving robust network hysteresis.
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Affiliation(s)
- James Scully
- Neuroscience Institute, Georgia State University, Atlanta, GA, United States
| | - Jassem Bourahmah
- Neuroscience Institute, Georgia State University, Atlanta, GA, United States
| | - David Bloom
- Neuroscience Institute, Georgia State University, Atlanta, GA, United States
- TReNDS Center, Georgia State University, Atlanta, GA, United States
| | - Andrey L Shilnikov
- Neuroscience Institute, Georgia State University, Atlanta, GA, United States
- Department of Mathematics and Statistics, Georgia State University, Atlanta, GA, United States
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2
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Piñeiro M, Mena W, Ewer J, Orio P. Extracting temporal relationships between weakly coupled peptidergic and motoneuronal signaling: Application to Drosophila ecdysis behavior. PLoS Comput Biol 2021; 17:e1008933. [PMID: 34910730 PMCID: PMC8716061 DOI: 10.1371/journal.pcbi.1008933] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2021] [Revised: 12/29/2021] [Accepted: 11/14/2021] [Indexed: 11/18/2022] Open
Abstract
Neuromodulators, such as neuropeptides, can regulate and reconfigure neural circuits to alter their output, affecting in this way animal physiology and behavior. The interplay between the activity of neuronal circuits, their modulation by neuropeptides, and the resulting behavior, is still poorly understood. Here, we present a quantitative framework to study the relationships between the temporal pattern of activity of peptidergic neurons and of motoneurons during Drosophila ecdysis behavior, a highly stereotyped motor sequence that is critical for insect growth. We analyzed, in the time and frequency domains, simultaneous intracellular calcium recordings of peptidergic CCAP (crustacean cardioactive peptide) neurons and motoneurons obtained from isolated central nervous systems throughout fictive ecdysis behavior induced ex vivo by Ecdysis triggering hormone. We found that the activity of both neuronal populations is tightly coupled in a cross-frequency manner, suggesting that CCAP neurons modulate the frequency of motoneuron firing. To explore this idea further, we used a probabilistic logistic model to show that calcium dynamics in CCAP neurons can predict the oscillation of motoneurons, both in a simple model and in a conductance-based model capable of simulating many features of the observed neural dynamics. Finally, we developed an algorithm to quantify the motor behavior observed in videos of pupal ecdysis, and compared their features to the patterns of neuronal calcium activity recorded ex vivo. We found that the motor activity of the intact animal is more regular than the motoneuronal activity recorded from ex vivo preparations during fictive ecdysis behavior; the analysis of the patterns of movement also allowed us to identify a new post-ecdysis phase.
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Affiliation(s)
- Miguel Piñeiro
- Centro Interdisciplinario de Neurociencia de Valparaíso, Universidad de Valparaíso, Valparaíso, Chile
| | - Wilson Mena
- Centro Interdisciplinario de Neurociencia de Valparaíso, Universidad de Valparaíso, Valparaíso, Chile
- Department of Neuroscience, Institut Pasteur, Paris, France
| | - John Ewer
- Centro Interdisciplinario de Neurociencia de Valparaíso, Universidad de Valparaíso, Valparaíso, Chile
- Instituto de Neurociencias, Facultad de Ciencias, Universidad de Valparaíso, Valparaíso, Chile
- * E-mail: (JE); (PO)
| | - Patricio Orio
- Centro Interdisciplinario de Neurociencia de Valparaíso, Universidad de Valparaíso, Valparaíso, Chile
- Instituto de Neurociencias, Facultad de Ciencias, Universidad de Valparaíso, Valparaíso, Chile
- * E-mail: (JE); (PO)
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3
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Protachevicz PR, Hansen M, Iarosz KC, Caldas IL, Batista AM, Kurths J. Emergence of Neuronal Synchronisation in Coupled Areas. Front Comput Neurosci 2021; 15:663408. [PMID: 33967729 PMCID: PMC8100315 DOI: 10.3389/fncom.2021.663408] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2021] [Accepted: 03/29/2021] [Indexed: 11/13/2022] Open
Abstract
One of the most fundamental questions in the field of neuroscience is the emergence of synchronous behaviour in the brain, such as phase, anti-phase, and shift-phase synchronisation. In this work, we investigate how the connectivity between brain areas can influence the phase angle and the neuronal synchronisation. To do this, we consider brain areas connected by means of excitatory and inhibitory synapses, in which the neuron dynamics is given by the adaptive exponential integrate-and-fire model. Our simulations suggest that excitatory and inhibitory connections from one area to another play a crucial role in the emergence of these types of synchronisation. Thus, in the case of unidirectional interaction, we observe that the phase angles of the neurons in the receiver area depend on the excitatory and inhibitory synapses which arrive from the sender area. Moreover, when the neurons in the sender area are synchronised, the phase angle variability of the receiver area can be reduced for some conductance values between the areas. For bidirectional interactions, we find that phase and anti-phase synchronisation can emerge due to excitatory and inhibitory connections. We also verify, for a strong inhibitory-to-excitatory interaction, the existence of silent neuronal activities, namely a large number of excitatory neurons that remain in silence for a long time.
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Affiliation(s)
- Paulo R Protachevicz
- Applied Physics Department, Institute of Physics, University of São Paulo, São Paulo, Brazil
| | - Matheus Hansen
- Computer Science Department, Institute of Science and Technology, Federal University of São Paulo - UNIFESP, São José dos Campos, Brazil
| | - Kelly C Iarosz
- Applied Physics Department, Institute of Physics, University of São Paulo, São Paulo, Brazil.,Faculdade de Telêmaco Borba, Telêmaco Borba, Brazil.,Graduate Program in Chemical Engineering, Federal University of Technology Paraná, Ponta Grossa, Brazil
| | - Iberê L Caldas
- Applied Physics Department, Institute of Physics, University of São Paulo, São Paulo, Brazil
| | - Antonio M Batista
- Applied Physics Department, Institute of Physics, University of São Paulo, São Paulo, Brazil.,Department of Mathematics and Statistics, State University of Ponta Grossa, Ponta Grossa, Brazil
| | - Jürgen Kurths
- Department Complexity Science, Potsdam Institute for Climate Impact Research, Potsdam, Germany.,Department of Physics, Humboldt University, Berlin, Germany.,Centre for Analysis of Complex Systems, Sechenov First Moscow State Medical University, Moscow, Russia
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4
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Collens J, Pusuluri K, Kelley A, Knapper D, Xing T, Basodi S, Alacam D, Shilnikov AL. Dynamics and bifurcations in multistable 3-cell neural networks. CHAOS (WOODBURY, N.Y.) 2020; 30:072101. [PMID: 32752614 DOI: 10.1063/5.0011374] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/20/2020] [Accepted: 07/04/2020] [Indexed: 06/11/2023]
Abstract
We disclose the generality of the intrinsic mechanisms underlying multistability in reciprocally inhibitory 3-cell circuits composed of simplified, low-dimensional models of oscillatory neurons, as opposed to those of a detailed Hodgkin-Huxley type [Wojcik et al., PLoS One 9, e92918 (2014)]. The computational reduction to return maps for the phase-lags between neurons reveals a rich multiplicity of rhythmic patterns in such circuits. We perform a detailed bifurcation analysis to show how such rhythms can emerge, disappear, and gain or lose stability, as the parameters of the individual cells and the synapses are varied.
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Affiliation(s)
- J Collens
- Neuroscience Institute, Georgia State University, Atlanta, Georgia 30303, USA
| | - K Pusuluri
- Neuroscience Institute, Georgia State University, Atlanta, Georgia 30303, USA
| | - A Kelley
- Neuroscience Institute, Georgia State University, Atlanta, Georgia 30303, USA
| | - D Knapper
- Neuroscience Institute, Georgia State University, Atlanta, Georgia 30303, USA
| | - T Xing
- Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia 30303, USA
| | - S Basodi
- Department of Computer Science, Georgia State University, Atlanta, Georgia 30303, USA
| | - D Alacam
- Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia 30303, USA
| | - A L Shilnikov
- Neuroscience Institute, Georgia State University, Atlanta, Georgia 30303, USA
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5
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Han F, Gu X, Wang Z, Fan H, Cao J, Lu Q. Global firing rate contrast enhancement in E/I neuronal networks by recurrent synchronized inhibition. CHAOS (WOODBURY, N.Y.) 2018; 28:106324. [PMID: 30384624 DOI: 10.1063/1.5037207] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/22/2018] [Accepted: 09/26/2018] [Indexed: 06/08/2023]
Abstract
Inhibitory synchronization is commonly observed and may play some important functional roles in excitatory/inhibitory (E/I) neuronal networks. The firing rate contrast enhancement is a general feature of information processing in sensory pathways, and a new mechanism of contrast enhancement by inhibitory synchronization in E/I neuronal networks is investigated in this paper. Inspired by the firing rate contrast enhancement phenomenon by the lateral feed-forward inhibition, we reveal that the firing rate contrast enhancement could also occur by recurrent inhibition in E/I networks. It is further found that the synchronized inhibitory neurons act as a global inhibition which can enhance the firing rate contrast of excitatory neurons globally in synchronized E/I networks, even in partially synchronous states. Therefore, the firing rate contrast enhancement might be an important function of inhibitory synchronization and might facilitate information transmission in neural systems.
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Affiliation(s)
- Fang Han
- College of Information Science and Technology, Donghua University, Shanghai 201620, People's Republic of China
| | - Xiaochun Gu
- College of Information Science and Technology, Donghua University, Shanghai 201620, People's Republic of China
| | - Zhijie Wang
- College of Information Science and Technology, Donghua University, Shanghai 201620, People's Republic of China
| | - Hong Fan
- Glorious Sun School of Business and Management, Donghua University, Shanghai 200051, People's Republic of China
| | - Jinfeng Cao
- College of Information Science and Technology, Donghua University, Shanghai 201620, People's Republic of China
| | - Qishao Lu
- School of Science, Beihang University, Beijing 100191, People's Republic of China
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6
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Thoby-Brisson M. Neural mechanisms for sigh generation during prenatal development. J Neurophysiol 2018; 120:1162-1172. [PMID: 29897860 DOI: 10.1152/jn.00314.2018] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022] Open
Abstract
The respiratory network of the preBötzinger complex (preBötC), which controls inspiratory behavior, can in normal conditions simultaneously produce two types of inspiration-related rhythmic activities: the eupneic rhythm composed of monophasic, low-amplitude, and relatively high-frequency bursts, interspersed with sigh rhythmic activity, composed of biphasic, high-amplitude, and lower frequency bursts. By combining electrophysiological recordings from transverse brainstem slices with computational modeling, new advances in the mechanisms underlying sigh production have been obtained during prenatal development. The present review summarizes recent findings that establish when sigh rhythmogenesis starts to be produced during embryonic development as well as the cellular, membrane, and synaptic properties required for its expression. Together, the results demonstrate that although generated by the same network, the eupnea and sigh rhythms have different developmental onset times and rely on distinct network properties. Because sighs (also known as augmented breaths) are important in maintaining lung function (by reopening collapsed alveoli), gaining insight into their underlying neural mechanisms at early developmental stages is likely to help in the treatment of prematurely born babies often suffering from breathing deficiencies.
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Affiliation(s)
- Muriel Thoby-Brisson
- Institut de Neurosciences Cognitives et Intégratives d'Aquitaine, CNRS UMR 5287, Université de Bordeaux , Bordeaux , France
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7
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Patel M, Joshi B. Deterministic stability regimes and noise-induced quasistable behavior in a pair of reciprocally inhibitory neurons. J Theor Biol 2018; 441:68-83. [PMID: 29330054 DOI: 10.1016/j.jtbi.2017.12.011] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2017] [Revised: 11/24/2017] [Accepted: 12/11/2017] [Indexed: 10/18/2022]
Abstract
Reciprocal inhibition is a common motif exploited by neuronal networks; an intuitive and tractable way to examine the behaviors produced by reciprocal inhibition is to consider a pair of neurons that synaptically inhibit each other and receive constant or noisy excitatory driving currents. In this work, we examine reciprocal inhibition using two models (a voltage-based and a current-based integrate-and-fire model with instantaneous or temporally structured input), and we use analytic and computational tools to examine the bifurcations that occur and study the various possible monostable, bistable, and tristable regimes that can exist; we find that, depending on system parameters (and on choice of neuron model), there can exist up to 3 distinct monostable regimes (denoted M0, M1, M2), 3 distinct bistable regimes (denoted B, B1, B2), and a single tristable regime (denoted T). We also find that synaptic inhibition exerts independent control over the two neurons - inhibition from neuron 1 to neuron 2 governs the spiking behavior of neuron 2 but has no impact on the spiking behavior of neuron 1 (and vice versa). The excitatory driving current, however, does not exhibit this property - the excitatory current to neuron 1 affects the spiking behavior of both neurons 1 and 2 (as does the excitatory current to neuron 2). Furthermore, we develop a methodology to examine the behavior of the system when the excitatory driving currents are allowed to be noisy, and we investigate the relationship between the behavior of the noisy system with the stability regime of the corresponding deterministic system.
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Affiliation(s)
- Mainak Patel
- Department of Mathematics, College of William and Mary, United States.
| | - Badal Joshi
- Department of Mathematics, California State University San Marcos, United States
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Reimbayev R, Daley K, Belykh I. When two wrongs make a right: synchronized neuronal bursting from combined electrical and inhibitory coupling. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2017; 375:rsta.2016.0282. [PMID: 28507227 PMCID: PMC5434073 DOI: 10.1098/rsta.2016.0282] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 03/08/2017] [Indexed: 05/24/2023]
Abstract
Synchronized cortical activities in the central nervous systems of mammals are crucial for sensory perception, coordination and locomotory function. The neuronal mechanisms that generate synchronous synaptic inputs in the neocortex are far from being fully understood. In this paper, we study the emergence of synchronization in networks of bursting neurons as a highly non-trivial, combined effect of electrical and inhibitory connections. We report a counterintuitive find that combined electrical and inhibitory coupling can synergistically induce robust synchronization in a range of parameters where electrical coupling alone promotes anti-phase spiking and inhibition induces anti-phase bursting. We reveal the underlying mechanism, which uses a balance between hidden properties of electrical and inhibitory coupling to act together to synchronize neuronal bursting. We show that this balance is controlled by the duty cycle of the self-coupled system which governs the synchronized bursting rhythm.This article is part of the themed issue 'Mathematical methods in medicine: neuroscience, cardiology and pathology'.
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Affiliation(s)
- Reimbay Reimbayev
- Department of Mathematics and Statistics and Neuroscience Institute, Georgia State University, 30 Pryor Street, Atlanta, GA 30303, USA
| | - Kevin Daley
- Department of Mathematics and Statistics and Neuroscience Institute, Georgia State University, 30 Pryor Street, Atlanta, GA 30303, USA
| | - Igor Belykh
- Department of Mathematics and Statistics and Neuroscience Institute, Georgia State University, 30 Pryor Street, Atlanta, GA 30303, USA
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Gunaratne CA, Sakurai A, Katz PS. Variations on a theme: species differences in synaptic connectivity do not predict central pattern generator activity. J Neurophysiol 2017; 118:1123-1132. [PMID: 28539397 DOI: 10.1152/jn.00203.2017] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2017] [Revised: 05/02/2017] [Accepted: 05/23/2017] [Indexed: 11/22/2022] Open
Abstract
A fundamental question in comparative neuroethology is the extent to which synaptic wiring determines behavior vs. the extent to which it is constrained by phylogeny. We investigated this by examining the connectivity and activity of homologous neurons in different species. Melibe leonina and Dendronotus iris (Mollusca, Gastropoda, Nudibranchia) have homologous neurons and exhibit homologous swimming behaviors consisting of alternating left-right (LR) whole body flexions. Yet, a homologous interneuron (Si1) differs between the two species in its participation in the swim motor pattern (SMP) and synaptic connectivity. In this study we examined Si1 homologs in two additional nudibranchs: Flabellina iodinea, which evolved LR swimming independently of Melibe and Dendronotus, and Tritonia diomedea, which swims with dorsal-ventral (DV) body flexions. In Flabellina, the contralateral Si1s exhibit alternating rhythmic bursting activity during the SMP and are members of the swim central pattern generator (CPG), as in Melibe The Si1 homologs in Tritonia do not burst rhythmically during the DV SMP but are inhibited and receive bilaterally synchronous synaptic input. In both Flabellina and Tritonia, the Si1 homologs exhibit reciprocal inhibition, as in Melibe However, in Flabellina the inhibition is polysynaptic, whereas in Tritonia it is monosynaptic, as in Melibe In all species, the contralateral Si1s are electrically coupled. These results suggest that Flabellina and Melibe convergently evolved a swim CPG that contains Si1; however, they differ in monosynaptic connections. Connectivity is more similar between Tritonia and Melibe, which exhibit different swimming behaviors. Thus connectivity between homologous neurons varies independently of both behavior and phylogeny.NEW & NOTEWORTHY This research shows that the synaptic connectivity between homologous neurons exhibits species-specific variations on a basic theme. The neurons vary in the extent of electrical coupling and reciprocal inhibition. They also exhibit different patterns of activity during rhythmic motor behaviors that are not predicted by their circuitry. The circuitry does not map onto the phylogeny in a predictable fashion either. Thus neither neuronal homology nor species behavior is predictive of neural circuit connectivity.
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Affiliation(s)
| | - Akira Sakurai
- Neuroscience Institute, Georgia State University, Atlanta, Georgia
| | - Paul S Katz
- Neuroscience Institute, Georgia State University, Atlanta, Georgia
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Kumar R, Bilal S, Ramaswamy R. Synchronization properties of coupled chaotic neurons: The role of random shared input. CHAOS (WOODBURY, N.Y.) 2016; 26:063118. [PMID: 27368783 DOI: 10.1063/1.4954377] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Spike-time correlations of neighbouring neurons depend on their intrinsic firing properties as well as on the inputs they share. Studies have shown that periodically firing neurons, when subjected to random shared input, exhibit asynchronicity. Here, we study the effect of random shared input on the synchronization of weakly coupled chaotic neurons. The cases of so-called electrical and chemical coupling are both considered, and we observe a wide range of synchronization behaviour. When subjected to identical shared random input, there is a decrease in the threshold coupling strength needed for chaotic neurons to synchronize in-phase. The system also supports lag-synchronous states, and for these, we find that shared input can cause desynchronization. We carry out a master stability function analysis for a network of such neurons and show agreement with the numerical simulations. The contrasting role of shared random input for complete and lag synchronized neurons is useful in understanding spike-time correlations observed in many areas of the brain.
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Affiliation(s)
- Rupesh Kumar
- School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| | - Shakir Bilal
- Department of Physics and Astrophysics, University of Delhi, Delhi 110 007, India
| | - Ram Ramaswamy
- School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi 110067, India
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11
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Shilnikov AL, Maurer AP. The Art of Grid Fields: Geometry of Neuronal Time. Front Neural Circuits 2016; 10:12. [PMID: 27013981 PMCID: PMC4782041 DOI: 10.3389/fncir.2016.00012] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2015] [Accepted: 02/19/2016] [Indexed: 11/13/2022] Open
Abstract
The discovery of grid cells in the entorhinal cortex has both elucidated our understanding of spatial representations in the brain, and germinated a large number of theoretical models regarding the mechanisms of these cells' striking spatial firing characteristics. These models cross multiple neurobiological levels that include intrinsic membrane resonance, dendritic integration, after hyperpolarization characteristics and attractor dynamics. Despite the breadth of the models, to our knowledge, parallels can be drawn between grid fields and other temporal dynamics observed in nature, much of which was described by Art Winfree and colleagues long before the initial description of grid fields. Using theoretical and mathematical investigations of oscillators, in a wide array of mediums far from the neurobiology of grid cells, Art Winfree has provided a substantial amount of research with significant and profound similarities. These theories provide specific inferences into the biological mechanisms and extraordinary resemblances across phenomenon. Therefore, this manuscript provides a novel interpretation on the phenomenon of grid fields, from the perspective of coupled oscillators, postulating that grid fields are the spatial representation of phase resetting curves in the brain. In contrast to prior models of gird cells, the current manuscript provides a sketch by which a small network of neurons, each with oscillatory components can operate to form grid cells, perhaps providing a unique hybrid between the competing attractor neural network and oscillatory interference models. The intention of this new interpretation of the data is to encourage novel testable hypotheses.
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Affiliation(s)
- Andrey L. Shilnikov
- Neuroscience Institute and Department of Mathematics and Statistics, Georgia State UniversityAtlanta, GA, USA
- Institute for Information Technology, Mathematics and Mechanics, Lobachevsky State University of Nizhni NovgorodNizhni Novgorod, Russia
| | - Andrew Porter Maurer
- Department of Neuroscience, McKnight Brain Institute, College of Medicine, University of FloridaGainesville, FL, USA
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Gu H, Zhao Z. Dynamics of Time Delay-Induced Multiple Synchronous Behaviors in Inhibitory Coupled Neurons. PLoS One 2015; 10:e0138593. [PMID: 26394224 PMCID: PMC4578859 DOI: 10.1371/journal.pone.0138593] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2015] [Accepted: 09/01/2015] [Indexed: 11/28/2022] Open
Abstract
The inhibitory synapse can induce synchronous behaviors different from the anti-phase synchronous behaviors, which have been reported in recent studies. In the present paper, synchronous behaviors are investigated in the motif model composed of reciprocal inhibitory coupled neurons with endogenous bursting and time delay. When coupling strength is weak, synchronous behavior appears at a single interval of time delay within a bursting period. When coupling strength is strong, multiple synchronous behaviors appear at different intervals of time delay within a bursting period. The different bursting patterns of synchronous behaviors, and time delays and coupling strengths that can induce the synchronous bursting patterns can be well interpreted by the dynamics of the endogenous bursting pattern of isolated neuron, which is acquired by the fast-slow dissection method, combined with the inhibitory coupling current. For an isolated neuron, when a negative impulsive current with suitable strength is applied at different phases of the bursting, multiple different bursting patterns can be induced. For a neuron in the motif, the inhibitory coupling current, of which the application time and strength is modulated by time delay and coupling strength, can cause single or multiple synchronous firing patterns like the negative impulsive current when time delay and coupling strength is suitable. The difference compared to the previously reported multiple synchronous behaviors that appear at time delays wider than a period of the endogenous firing is discussed. The results present novel examples of synchronous behaviors in the neuronal network with inhibitory synapses and provide a reasonable explanation.
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Affiliation(s)
- Huaguang Gu
- School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China
- * E-mail:
| | - Zhiguo Zhao
- School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China
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13
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Belykh I, Reimbayev R, Zhao K. Synergistic effect of repulsive inhibition in synchronization of excitatory networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:062919. [PMID: 26172784 DOI: 10.1103/physreve.91.062919] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2014] [Indexed: 06/04/2023]
Abstract
We show that the addition of pairwise repulsive inhibition to excitatory networks of bursting neurons induces synchrony, in contrast to one's expectations. Through stability analysis, we reveal the mechanism underlying this purely synergistic phenomenon and demonstrate that it originates from the transition between different types of bursting, caused by excitatory-inhibitory synaptic coupling. This effect is generic and observed in different models of bursting neurons and fast synaptic interactions. We also find a universal scaling law for the synchronization stability condition for large networks in terms of the number of excitatory and inhibitory inputs each neuron receives, regardless of the network size and topology. This general law is in sharp contrast with linearly coupled networks with positive (attractive) and negative (repulsive) coupling where the placement and structure of negative connections heavily affect synchronization.
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Affiliation(s)
- Igor Belykh
- Department of Mathematics and Statistics and Neuroscience Institute, Georgia State University, 30 Pryor Street, Atlanta, Georgia 30303, USA
| | - Reimbay Reimbayev
- Department of Mathematics and Statistics and Neuroscience Institute, Georgia State University, 30 Pryor Street, Atlanta, Georgia 30303, USA
| | - Kun Zhao
- Department of Mathematics and Statistics and Neuroscience Institute, Georgia State University, 30 Pryor Street, Atlanta, Georgia 30303, USA
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14
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Wojcik J, Schwabedal J, Clewley R, Shilnikov AL. Key bifurcations of bursting polyrhythms in 3-cell central pattern generators. PLoS One 2014; 9:e92918. [PMID: 24739943 PMCID: PMC3989192 DOI: 10.1371/journal.pone.0092918] [Citation(s) in RCA: 53] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2014] [Accepted: 02/27/2014] [Indexed: 11/24/2022] Open
Abstract
We identify and describe the key qualitative rhythmic states in various 3-cell network motifs of a multifunctional central pattern generator (CPG). Such CPGs are neural microcircuits of cells whose synergetic interactions produce multiple states with distinct phase-locked patterns of bursting activity. To study biologically plausible CPG models, we develop a suite of computational tools that reduce the problem of stability and existence of rhythmic patterns in networks to the bifurcation analysis of fixed points and invariant curves of a Poincaré return maps for phase lags between cells. We explore different functional possibilities for motifs involving symmetry breaking and heterogeneity. This is achieved by varying coupling properties of the synapses between the cells and studying the qualitative changes in the structure of the corresponding return maps. Our findings provide a systematic basis for understanding plausible biophysical mechanisms for the regulation of rhythmic patterns generated by various CPGs in the context of motor control such as gait-switching in locomotion. Our analysis does not require knowledge of the equations modeling the system and provides a powerful qualitative approach to studying detailed models of rhythmic behavior. Thus, our approach is applicable to a wide range of biological phenomena beyond motor control.
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Affiliation(s)
- Jeremy Wojcik
- Applied Technology Associates, Albuquerque, New Mexico, United States of America
| | - Justus Schwabedal
- Neuroscience Institute, Georgia State University, Atlanta, Georgia, United States of America
| | - Robert Clewley
- Neuroscience Institute, Georgia State University, Atlanta, Georgia, United States of America
- Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia, United States of America
| | - Andrey L. Shilnikov
- Neuroscience Institute, Georgia State University, Atlanta, Georgia, United States of America
- Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia, United States of America
- Department of Computational Mathematics and Cybernetics, Lobachevsky State University of Nizhni Novgorod, Nizhni Novgorod, Russia
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15
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Juang J, Liang YH. Cluster synchronization in networks of neurons with chemical synapses. CHAOS (WOODBURY, N.Y.) 2014; 24:013110. [PMID: 24697372 DOI: 10.1063/1.4862484] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
In this work, we study the cluster synchronization of chemically coupled and generally formulated networks which are allowed to be nonidentical. The sufficient condition for the existence of stably synchronous clusters is derived. Specifically, we only need to check the stability of the origins of m decoupled linear systems. Here, m is the number of subpopulations. Examples of nonidentical networks such as Hindmarsh-Rose (HR) neurons with various choices of parameters in different subpopulations, or HR neurons in one subpopulation and FitzHugh-Nagumo neurons in the other subpopulation are provided. Explicit threshold for the coupling strength that guarantees the stably cluster synchronization can be obtained.
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Affiliation(s)
- Jonq Juang
- Department of Applied Mathematics, and Center of Mathematics Modeling and Scientific Computing, National Chiao Tung University, Hsinchu, Taiwan and National Center for Theoretical Sciences, Hsinchu, Taiwan
| | - Yu-Hao Liang
- Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan
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16
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Jalil S, Allen D, Youker J, Shilnikov A. Toward robust phase-locking in Melibe swim central pattern generator models. CHAOS (WOODBURY, N.Y.) 2013; 23:046105. [PMID: 24387584 DOI: 10.1063/1.4825389] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Small groups of interneurons, abbreviated by CPG for central pattern generators, are arranged into neural networks to generate a variety of core bursting rhythms with specific phase-locked states, on distinct time scales, which govern vital motor behaviors in invertebrates such as chewing and swimming. These movements in lower level animals mimic motions of organs in higher animals due to evolutionarily conserved mechanisms. Hence, various neurological diseases can be linked to abnormal movement of body parts that are regulated by a malfunctioning CPG. In this paper, we, being inspired by recent experimental studies of neuronal activity patterns recorded from a swimming motion CPG of the sea slug Melibe leonina, examine a mathematical model of a 4-cell network that can plausibly and stably underlie the observed bursting rhythm. We develop a dynamical systems framework for explaining the existence and robustness of phase-locked states in activity patterns produced by the modeled CPGs. The proposed tools can be used for identifying core components for other CPG networks with reliable bursting outcomes and specific phase relationships between the interneurons. Our findings can be employed for identifying or implementing the conditions for normal and pathological functioning of basic CPGs of animals and artificially intelligent prosthetics that can regulate various movements.
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Affiliation(s)
- Sajiya Jalil
- Neuroscience Institute and Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia 30303, USA
| | - Dane Allen
- Neuroscience Institute and Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia 30303, USA
| | - Joseph Youker
- Neuroscience Institute and Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia 30303, USA
| | - Andrey Shilnikov
- Neuroscience Institute and Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia 30303, USA
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Ramirez JM, Doi A, Garcia AJ, Elsen FP, Koch H, Wei AD. The cellular building blocks of breathing. Compr Physiol 2013; 2:2683-731. [PMID: 23720262 DOI: 10.1002/cphy.c110033] [Citation(s) in RCA: 48] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023]
Abstract
Respiratory brainstem neurons fulfill critical roles in controlling breathing: they generate the activity patterns for breathing and contribute to various sensory responses including changes in O2 and CO2. These complex sensorimotor tasks depend on the dynamic interplay between numerous cellular building blocks that consist of voltage-, calcium-, and ATP-dependent ionic conductances, various ionotropic and metabotropic synaptic mechanisms, as well as neuromodulators acting on G-protein coupled receptors and second messenger systems. As described in this review, the sensorimotor responses of the respiratory network emerge through the state-dependent integration of all these building blocks. There is no known respiratory function that involves only a small number of intrinsic, synaptic, or modulatory properties. Because of the complex integration of numerous intrinsic, synaptic, and modulatory mechanisms, the respiratory network is capable of continuously adapting to changes in the external and internal environment, which makes breathing one of the most integrated behaviors. Not surprisingly, inspiration is critical not only in the control of ventilation, but also in the context of "inspiring behaviors" such as arousal of the mind and even creativity. Far-reaching implications apply also to the underlying network mechanisms, as lessons learned from the respiratory network apply to network functions in general.
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Affiliation(s)
- J M Ramirez
- Center for Integrative Brain Research, Seattle Children's Research Institut, Seattle, Washington, USA.
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18
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Switching mechanisms and bout times in a pair of reciprocally inhibitory neurons. J Comput Neurosci 2013; 36:177-91. [DOI: 10.1007/s10827-013-0464-6] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2012] [Accepted: 05/20/2013] [Indexed: 01/22/2023]
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19
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Carroll MS, Viemari JC, Ramirez JM. Patterns of inspiratory phase-dependent activity in the in vitro respiratory network. J Neurophysiol 2012; 109:285-95. [PMID: 23076109 DOI: 10.1152/jn.00619.2012] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022] Open
Abstract
Mechanistic descriptions of rhythmogenic neural networks have often relied on ball-and-stick diagrams, which define interactions between functional classes of cells assumed to be reasonably homogenous. Application of this formalism to networks underlying respiratory rhythm generation in mammals has produced increasingly intricate models that have generated significant insight, but the underlying assumption that individual cells within these network fall into distinct functional classes has not been rigorously tested. In the present study we used multiunit extracellular recording in the in vitro pre-Bötzinger complex to identify and characterize the rhythmic activity of 951 cells. Inspiratory phase-dependent activity was estimated for all cells, and the data set as a whole was analyzed with principal component analysis, nonlinear dimensionality reduction, and hierarchical clustering techniques. None of these techniques revealed categorically distinct functional cell classes, indicating instead that the behavior of these cells within the network falls along several continua of spiking behavior.
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Affiliation(s)
- Michael S Carroll
- Center for Integrative Brain Research, Seattle Children's Research Institute, Seattle, WA 98101, USA.
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21
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Jalil S, Belykh I, Shilnikov A. Spikes matter for phase-locked bursting in inhibitory neurons. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:036214. [PMID: 22587168 DOI: 10.1103/physreve.85.036214] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2011] [Revised: 12/20/2011] [Indexed: 05/31/2023]
Abstract
We show that inhibitory networks composed of two endogenously bursting neurons can robustly display several coexistent phase-locked states in addition to stable antiphase and in-phase bursting. This work complements and enhances our recent result [Jalil, Belykh, and Shilnikov, Phys. Rev. E 81, 045201(R) (2010)] that fast reciprocal inhibition can synchronize bursting neurons due to spike interactions. We reveal the role of spikes in generating multiple phase-locked states and demonstrate that this multistability is generic by analyzing diverse models of bursting networks with various fast inhibitory synapses; the individual cell models include the reduced leech heart interneuron, the Sherman model for pancreatic beta cells, and the Purkinje neuron model.
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Affiliation(s)
- Sajiya Jalil
- Department of Mathematics and Statistics, Georgia State University, 30 Pryor Street, Atlanta, Georgia 30303, USA
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Srinivasan K, Senthilkumar DV, Murali K, Lakshmanan M, Kurths J. Synchronization transitions in coupled time-delay electronic circuits with a threshold nonlinearity. CHAOS (WOODBURY, N.Y.) 2011; 21:023119. [PMID: 21721761 DOI: 10.1063/1.3591791] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Experimental observations of typical kinds of synchronization transitions are reported in unidirectionally coupled time-delay electronic circuits with a threshold nonlinearity and two time delays, namely feedback delay τ(1) and coupling delay τ(2). We have observed transitions from anticipatory to lag via complete synchronization and their inverse counterparts with excitatory and inhibitory couplings, respectively, as a function of the coupling delay τ(2). The anticipating and lag times depend on the difference between the feedback and the coupling delays. A single stability condition for all the different types of synchronization is found to be valid as the stability condition is independent of both the delays. Further, the existence of different kinds of synchronizations observed experimentally is corroborated by numerical simulations and from the changes in the Lyapunov exponents of the coupled time-delay systems.
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Affiliation(s)
- K Srinivasan
- Centre for Nonlinear Dynamics, Department of Physics, Bharathidasan University, Tiruchirapalli 620024, India
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Adhikari BM, Prasad A, Dhamala M. Time-delay-induced phase-transition to synchrony in coupled bursting neurons. CHAOS (WOODBURY, N.Y.) 2011; 21:023116. [PMID: 21721758 DOI: 10.1063/1.3584822] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Signal transmission time delays in a network of nonlinear oscillators are known to be responsible for a variety of interesting dynamic behaviors including phase-flip transitions leading to synchrony or out of synchrony. Here, we uncover that phase-flip transitions are general phenomena and can occur in a network of coupled bursting neurons with a variety of coupling types. The transitions are marked by nonlinear changes in both temporal and phase-space characteristics of the coupled system. We demonstrate these phase-transitions with Hindmarsh-Rose and Leech-Heart interneuron models and discuss the implications of these results in understanding collective dynamics of bursting neurons in the brain.
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Affiliation(s)
- Bhim Mani Adhikari
- Department of Physics and Astronomy, Georgia State University, Atlanta, Georgia 30303, USA
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24
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Belykh I, Hasler M. Mesoscale and clusters of synchrony in networks of bursting neurons. CHAOS (WOODBURY, N.Y.) 2011; 21:016106. [PMID: 21456848 DOI: 10.1063/1.3563581] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We study the role of network architecture in the formation of synchronous clusters in synaptically coupled networks of bursting neurons. We give a simple combinatorial algorithm that finds the largest synchronous clusters from the network topology. We demonstrate that networks with a certain degree of internal symmetries are likely to have cluster decompositions with relatively large clusters, leading potentially to cluster synchronization at the mesoscale network level. We also address the asymptotic stability of cluster synchronization in excitatory networks of Hindmarsh-Rose bursting neurons and derive explicit thresholds for the coupling strength that guarantees stable cluster synchronization.
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Affiliation(s)
- Igor Belykh
- Department of Mathematics and Statistics and Neuroscience Institute, Georgia State University, 30 Pryor Street, Atlanta, Georgia 30303, USA
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