1
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Galvis D, Hodson DJ, Wedgwood KC. Spatial distribution of heterogeneity as a modulator of collective dynamics in pancreatic beta-cell networks and beyond. FRONTIERS IN NETWORK PHYSIOLOGY 2023; 3:fnetp.2023.1170930. [PMID: 36987428 PMCID: PMC7614376 DOI: 10.3389/fnetp.2023.1170930] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Indexed: 03/30/2023]
Abstract
We study the impact of spatial distribution of heterogeneity on collective dynamics in gap-junction coupled beta-cell networks comprised on cells from two populations that differ in their intrinsic excitability. Initially, these populations are uniformly and randomly distributed throughout the networks. We develop and apply an iterative algorithm for perturbing the arrangement of the network such that cells from the same population are increasingly likely to be adjacent to one another. We find that the global input strength, or network drive, necessary to transition the network from a state of quiescence to a state of synchronised and oscillatory activity decreases as network sortedness increases. Moreover, for weak coupling, we find that regimes of partial synchronisation and wave propagation arise, which depend both on network drive and network sortedness. We then demonstrate the utility of this algorithm for studying the distribution of heterogeneity in general networks, for which we use Watts-Strogatz networks as a case study. This work highlights the importance of heterogeneity in node dynamics in establishing collective rhythms in complex, excitable networks and has implications for a wide range of real-world systems that exhibit such heterogeneity.
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Affiliation(s)
- Daniel Galvis
- Centre for Systems Modelling and Quantitative Biomedicine, University of Birmingham, Birmingham, UK
- Institute of Metabolism and Systems Research (IMSR), University of Birmingham, Birmingham, UK
- Correspondence: Daniel Galvis,
| | - David J. Hodson
- Institute of Metabolism and Systems Research (IMSR), University of Birmingham, Birmingham, UK
- Centre of Membrane Proteins and Receptors (COMPARE), University of Birmingham, Birmingham, UK
- Oxford Centre for Diabetes, Endocrinology, and Metabolism (OCDEM), Churchill Hospital, Radcliffe Department of Medicine, University of Oxford, Oxford, UK
- NIHR Oxford Biomedical Research Centre, Churchill Hospital, Radcliffe Department of Medicine, University of Oxford, Oxford, UK
| | - Kyle C.A. Wedgwood
- Living Systems Institute, University of Exeter, Exeter, UK
- EPSRC Hub for Quantitative Modelling in Healthcare, University of Exeter, Exeter, UK
- College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, UK
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2
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Correlation Analysis of Synchronization Type and Degree in Respiratory Neural Network. COMPUTATIONAL INTELLIGENCE AND NEUROSCIENCE 2022; 2021:4475184. [PMID: 34987564 PMCID: PMC8723864 DOI: 10.1155/2021/4475184] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/07/2021] [Revised: 11/17/2021] [Accepted: 11/19/2021] [Indexed: 12/28/2022]
Abstract
Pre-Bötzinger complex (PBC) is a necessary condition for the generation of respiratory rhythm. Due to the existence of synaptic gaps, delay plays a key role in the synchronous operation of coupled neurons. In this study, the relationship between synchronization and correlation degree is established for the first time by using ISI bifurcation and correlation coefficient, and the relationship between synchronization and correlation degree is discussed under the conditions of no delay, symmetric delay, and asymmetric delay. The results show that the phase synchronization of two coupling PBCs is closely related to the weak correlation, that is, the weak phase synchronization may occur under the condition of incomplete synchronization. Moreover, the time delay and coupling strength are controlled in the modified PBC network model, which not only reveals the law of PBC firing transition but also reveals the complex synchronization behavior in the coupled chaotic neurons. Especially, when the two coupled neurons are nonidentical, the complete synchronization will disappear. These results fully reveal the dynamic behavior of the PBC neural system, which is helpful to explore the signal transmission and coding of PBC neurons and provide theoretical value for further understanding respiratory rhythm.
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3
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Ramirez JM, Burgraff NJ, Wei AD, Baertsch NA, Varga AG, Baghdoyan HA, Lydic R, Morris KF, Bolser DC, Levitt ES. Neuronal mechanisms underlying opioid-induced respiratory depression: our current understanding. J Neurophysiol 2021; 125:1899-1919. [PMID: 33826874 DOI: 10.1152/jn.00017.2021] [Citation(s) in RCA: 37] [Impact Index Per Article: 12.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023] Open
Abstract
Opioid-induced respiratory depression (OIRD) represents the primary cause of death associated with therapeutic and recreational opioid use. Within the United States, the rate of death from opioid abuse since the early 1990s has grown disproportionally, prompting the classification as a nationwide "epidemic." Since this time, we have begun to unravel many fundamental cellular and systems-level mechanisms associated with opioid-related death. However, factors such as individual vulnerability, neuromodulatory compensation, and redundancy of opioid effects across central and peripheral nervous systems have created a barrier to a concise, integrative view of OIRD. Within this review, we bring together multiple perspectives in the field of OIRD to create an overarching viewpoint of what we know, and where we view this essential topic of research going forward into the future.
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Affiliation(s)
- Jan-Marino Ramirez
- Department of Neurological Surgery, University of Washington, Seattle, Washington.,Center for Integrative Brain Research, Seattle Children's Research Institute, Seattle, Washington
| | - Nicholas J Burgraff
- Center for Integrative Brain Research, Seattle Children's Research Institute, Seattle, Washington
| | - Aguan D Wei
- Center for Integrative Brain Research, Seattle Children's Research Institute, Seattle, Washington
| | - Nathan A Baertsch
- Center for Integrative Brain Research, Seattle Children's Research Institute, Seattle, Washington
| | - Adrienn G Varga
- Department of Pharmacology and Therapeutics, University of Florida, Gainesville, Florida.,Center for Respiratory Research and Rehabilitation, Department of Physical Therapy, University of Florida, Gainesville, Florida
| | - Helen A Baghdoyan
- Department of Psychology, University of Tennessee, Knoxville, Tennessee.,Oak Ridge National Laboratory, Oak Ridge, Tennessee
| | - Ralph Lydic
- Department of Psychology, University of Tennessee, Knoxville, Tennessee.,Oak Ridge National Laboratory, Oak Ridge, Tennessee
| | - Kendall F Morris
- Department of Molecular Pharmacology and Physiology, Morsani College of Medicine, University of South Florida, Tampa, Florida
| | - Donald C Bolser
- Department of Physiological Sciences, College of Veterinary Medicine, University of Florida, Gainesville, Florida
| | - Erica S Levitt
- Department of Pharmacology and Therapeutics, University of Florida, Gainesville, Florida.,Center for Respiratory Research and Rehabilitation, Department of Physical Therapy, University of Florida, Gainesville, Florida
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4
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Juárez-Vidales JDJ, Pérez-Ortega J, Lorea-Hernández JJ, Méndez-Salcido F, Peña-Ortega F. Configuration and dynamics of dominant inspiratory multineuronal activity patterns during eupnea and gasping generation in vitro. J Neurophysiol 2021; 125:1289-1306. [PMID: 33502956 DOI: 10.1152/jn.00563.2020] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Abstract
The pre-Bötzinger complex (preBötC), located within the ventral respiratory column, produces inspiratory bursts in varying degrees of synchronization/amplitude. This wide range of population burst patterns reflects the flexibility of the preBötC neurons, which is expressed in variations in the onset/offset times of their activations and their activity during the population bursts, with respiratory neurons exhibiting a large cycle-to-cycle timing jitter both at the population activity onset and at the population activity peak, suggesting that respiratory neurons are stochastically activated before and during the inspiratory bursts. However, it is still unknown whether this stochasticity is maintained while evaluating the coactivity of respiratory neuronal ensembles. Moreover, the preBötC topology also remains unknown. In this study, by simultaneously recording tens of preBötC neurons and using coactivation analysis during the inspiratory periods, we found that the preBötC has a scale-free configuration (mixture of not many highly connected nodes, hubs, with abundant poorly connected elements) exhibiting the rich-club phenomenon (hubs more likely interconnected with each other). PreBötC neurons also produce multineuronal activity patterns (MAPs) that are highly stable and change during the hypoxia-induced reconfiguration. Moreover, preBötC contains a coactivating core network shared by all its MAPs. Finally, we found a distinctive pattern of sequential coactivation of core network neurons at the beginning of the inspiratory periods, indicating that, when evaluated at the multicellular level, the coactivation of respiratory neurons seems not to be stochastic.NEW & NOTEWORTHY By means of multielectrode recordings of preBötC neurons, we evaluated their configuration in normoxia and hypoxia, finding that the preBötC exhibits a scale-free configuration with a rich-club phenomenon. preBötC neurons produce multineuronal activity patterns that are highly stable but change during hypoxia. The preBötC contains a coactivating core network that exhibit a distinctive pattern of coactivation at the beginning of inspirations. These results reveal some network basis of inspiratory rhythm generation and its reconfiguration during hypoxia.
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Affiliation(s)
- Josué de Jesús Juárez-Vidales
- Departamento de Neurobiología del Desarrollo y Neurofisiología, Instituto de Neurobiología, Universidad Nacional Autónoma de México, Queretaro, Mexico
| | - Jesús Pérez-Ortega
- Departamento de Neurobiología del Desarrollo y Neurofisiología, Instituto de Neurobiología, Universidad Nacional Autónoma de México, Queretaro, Mexico
| | - Jonathan Julio Lorea-Hernández
- Departamento de Neurobiología del Desarrollo y Neurofisiología, Instituto de Neurobiología, Universidad Nacional Autónoma de México, Queretaro, Mexico
| | - Felipe Méndez-Salcido
- Departamento de Neurobiología del Desarrollo y Neurofisiología, Instituto de Neurobiología, Universidad Nacional Autónoma de México, Queretaro, Mexico
| | - Fernando Peña-Ortega
- Departamento de Neurobiología del Desarrollo y Neurofisiología, Instituto de Neurobiología, Universidad Nacional Autónoma de México, Queretaro, Mexico
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5
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Montangie L, Miehl C, Gjorgjieva J. Autonomous emergence of connectivity assemblies via spike triplet interactions. PLoS Comput Biol 2020; 16:e1007835. [PMID: 32384081 PMCID: PMC7239496 DOI: 10.1371/journal.pcbi.1007835] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2019] [Revised: 05/20/2020] [Accepted: 03/31/2020] [Indexed: 01/08/2023] Open
Abstract
Non-random connectivity can emerge without structured external input driven by activity-dependent mechanisms of synaptic plasticity based on precise spiking patterns. Here we analyze the emergence of global structures in recurrent networks based on a triplet model of spike timing dependent plasticity (STDP), which depends on the interactions of three precisely-timed spikes, and can describe plasticity experiments with varying spike frequency better than the classical pair-based STDP rule. We derive synaptic changes arising from correlations up to third-order and describe them as the sum of structural motifs, which determine how any spike in the network influences a given synaptic connection through possible connectivity paths. This motif expansion framework reveals novel structural motifs under the triplet STDP rule, which support the formation of bidirectional connections and ultimately the spontaneous emergence of global network structure in the form of self-connected groups of neurons, or assemblies. We propose that under triplet STDP assembly structure can emerge without the need for externally patterned inputs or assuming a symmetric pair-based STDP rule common in previous studies. The emergence of non-random network structure under triplet STDP occurs through internally-generated higher-order correlations, which are ubiquitous in natural stimuli and neuronal spiking activity, and important for coding. We further demonstrate how neuromodulatory mechanisms that modulate the shape of the triplet STDP rule or the synaptic transmission function differentially promote structural motifs underlying the emergence of assemblies, and quantify the differences using graph theoretic measures. Emergent non-random connectivity structures in different brain regions are tightly related to specific patterns of neural activity and support diverse brain functions. For instance, self-connected groups of neurons, known as assemblies, have been proposed to represent functional units in brain circuits and can emerge even without patterned external instruction. Here we investigate the emergence of non-random connectivity in recurrent networks using a particular plasticity rule, triplet STDP, which relies on the interaction of spike triplets and can capture higher-order statistical dependencies in neural activity. We derive the evolution of the synaptic strengths in the network and explore the conditions for the self-organization of connectivity into assemblies. We demonstrate key differences of the triplet STDP rule compared to the classical pair-based rule in terms of how assemblies are formed, including the realistic asymmetric shape and influence of novel connectivity motifs on network plasticity driven by higher-order correlations. Assembly formation depends on the specific shape of the STDP window and synaptic transmission function, pointing towards an important role of neuromodulatory signals on formation of intrinsically generated assemblies.
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Affiliation(s)
- Lisandro Montangie
- Computation in Neural Circuits Group, Max Planck Institute for Brain Research, Frankfurt, Germany
| | - Christoph Miehl
- Computation in Neural Circuits Group, Max Planck Institute for Brain Research, Frankfurt, Germany
- Technical University of Munich, School of Life Sciences, Freising, Germany
| | - Julijana Gjorgjieva
- Computation in Neural Circuits Group, Max Planck Institute for Brain Research, Frankfurt, Germany
- Technical University of Munich, School of Life Sciences, Freising, Germany
- * E-mail:
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6
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Peña-Ortega F. Neural Network Reconfigurations: Changes of the Respiratory Network by Hypoxia as an Example. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2018; 1015:217-237. [PMID: 29080029 DOI: 10.1007/978-3-319-62817-2_12] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
Neural networks, including the respiratory network, can undergo a reconfiguration process by just changing the number, the connectivity or the activity of their elements. Those elements can be either brain regions or neurons, which constitute the building blocks of macrocircuits and microcircuits, respectively. The reconfiguration processes can also involve changes in the number of connections and/or the strength between the elements of the network. These changes allow neural networks to acquire different topologies to perform a variety of functions or change their responses as a consequence of physiological or pathological conditions. Thus, neural networks are not hardwired entities, but they constitute flexible circuits that can be constantly reconfigured in response to a variety of stimuli. Here, we are going to review several examples of these processes with special emphasis on the reconfiguration of the respiratory rhythm generator in response to different patterns of hypoxia, which can lead to changes in respiratory patterns or lasting changes in frequency and/or amplitude.
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Affiliation(s)
- Fernando Peña-Ortega
- Departamento de Neurobiología del Desarrollo y Neurofisiología, Instituto de Neurobiología, Universidad Nacional Autónoma de México, UNAM-Campus Juriquilla, Boulevard Juriquilla 3001, Querétaro, 76230, Mexico.
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7
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Harris KD, Dashevskiy T, Mendoza J, Garcia AJ, Ramirez JM, Shea-Brown E. Different roles for inhibition in the rhythm-generating respiratory network. J Neurophysiol 2017; 118:2070-2088. [PMID: 28615332 PMCID: PMC5626906 DOI: 10.1152/jn.00174.2017] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2017] [Revised: 05/25/2017] [Accepted: 06/12/2017] [Indexed: 12/20/2022] Open
Abstract
Unraveling the interplay of excitation and inhibition within rhythm-generating networks remains a fundamental issue in neuroscience. We use a biophysical model to investigate the different roles of local and long-range inhibition in the respiratory network, a key component of which is the pre-Bötzinger complex inspiratory microcircuit. Increasing inhibition within the microcircuit results in a limited number of out-of-phase neurons before rhythmicity and synchrony degenerate. Thus unstructured local inhibition is destabilizing and cannot support the generation of more than one rhythm. A two-phase rhythm requires restructuring the network into two microcircuits coupled by long-range inhibition in the manner of a half-center. In this context, inhibition leads to greater stability of the two out-of-phase rhythms. We support our computational results with in vitro recordings from mouse pre-Bötzinger complex. Partial excitation block leads to increased rhythmic variability, but this recovers after blockade of inhibition. Our results support the idea that local inhibition in the pre-Bötzinger complex is present to allow for descending control of synchrony or robustness to adverse conditions like hypoxia. We conclude that the balance of inhibition and excitation determines the stability of rhythmogenesis, but with opposite roles within and between areas. These different inhibitory roles may apply to a variety of rhythmic behaviors that emerge in widespread pattern-generating circuits of the nervous system.NEW & NOTEWORTHY The roles of inhibition within the pre-Bötzinger complex (preBötC) are a matter of debate. Using a combination of modeling and experiment, we demonstrate that inhibition affects synchrony, period variability, and overall frequency of the preBötC and coupled rhythmogenic networks. This work expands our understanding of ubiquitous motor and cognitive oscillatory networks.
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Affiliation(s)
| | - Tatiana Dashevskiy
- Center for Integrative Brain Research, Seattle Children's Research Institute, Seattle, Washington
| | - Joshua Mendoza
- Center for Integrative Brain Research, Seattle Children's Research Institute, Seattle, Washington
| | - Alfredo J Garcia
- Institute for Integrative Physiology and Section of Emergency Medicine, University of Chicago, Chicago, Illinois; and
| | - Jan-Marino Ramirez
- Center for Integrative Brain Research, Seattle Children's Research Institute, Seattle, Washington
- Department of Neurological Surgery, University of Washington School of Medicine, Seattle, Washington
| | - Eric Shea-Brown
- Department of Applied Mathematics, University of Washington, Seattle, Washington
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8
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Rubin JE. Computational models of basal ganglia dysfunction: the dynamics is in the details. Curr Opin Neurobiol 2017; 46:127-135. [PMID: 28888856 DOI: 10.1016/j.conb.2017.08.011] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2017] [Accepted: 08/22/2017] [Indexed: 12/18/2022]
Abstract
The development, simulation, and analysis of mathematical models offer helpful tools for integrating experimental findings and exploring or suggesting possible explanatory mechanisms. As models relating to basal ganglia dysfunction have proliferated, however, there has not always been consistency among their findings. This work points out several ways in which biological details, relating to ionic currents and synaptic pathways, can influence the dynamics of models of the basal ganglia under parkinsonian conditions and hence may be important for inclusion in models. It also suggests some additional useful directions for future modeling studies relating to basal ganglia dysfunction.
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Affiliation(s)
- Jonathan E Rubin
- Department of Mathematics and Center for the Neural Basis of Cognition, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA 15260, USA.
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9
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Oku Y, Hülsmann S. A computational model of the respiratory network challenged and optimized by data from optogenetic manipulation of glycinergic neurons. Neuroscience 2017; 347:111-122. [PMID: 28215988 DOI: 10.1016/j.neuroscience.2017.01.041] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2016] [Revised: 01/25/2017] [Accepted: 01/25/2017] [Indexed: 12/14/2022]
Abstract
The topology of the respiratory network in the brainstem has been addressed using different computational models, which help to understand the functional properties of the system. We tested a neural mass model by comparing the result of activation and inhibition of inhibitory neurons in silico with recently published results of optogenetic manipulation of glycinergic neurons [Sherman, et al. (2015) Nat Neurosci 18:408]. The comparison revealed that a five-cell type model consisting of three classes of inhibitory neurons [I-DEC, E-AUG, E-DEC (PI)] and two excitatory populations (pre-I/I) and (I-AUG) neurons can be applied to explain experimental observations made by stimulating or inhibiting inhibitory neurons by light sensitive ion channels.
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Affiliation(s)
- Yoshitaka Oku
- Department of Physiology, Hyogo College of Medicine, Nishinomiya, Hyogo 663-8501, Japan.
| | - Swen Hülsmann
- Clinic for Anesthesiology, University Hospital Göttingen, Göttingen 37099, Germany; DFG Research Center for Nanoscale Microscopy and Molecular Physiology of the Brain (CNMPB), Göttingen, Germany.
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10
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Lal A, Oku Y, Someya H, Miwakeichi F, Tamura Y. Emergent Network Topology within the Respiratory Rhythm-Generating Kernel Evolved In Silico. PLoS One 2016; 11:e0154049. [PMID: 27152967 PMCID: PMC4859517 DOI: 10.1371/journal.pone.0154049] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2015] [Accepted: 04/07/2016] [Indexed: 12/30/2022] Open
Abstract
We hypothesize that the network topology within the pre-Bötzinger Complex (preBötC), the mammalian respiratory rhythm generating kernel, is not random, but is optimized in the course of ontogeny/phylogeny so that the network produces respiratory rhythm efficiently and robustly. In the present study, we attempted to identify topology of synaptic connections among constituent neurons of the preBötC based on this hypothesis. To do this, we first developed an effective evolutionary algorithm for optimizing network topology of a neuronal network to exhibit a ‘desired characteristic’. Using this evolutionary algorithm, we iteratively evolved an in silico preBötC ‘model’ network with initial random connectivity to a network exhibiting optimized synchronous population bursts. The evolved ‘idealized’ network was then analyzed to gain insight into: (1) optimal network connectivity among different kinds of neurons—excitatory as well as inhibitory pacemakers, non-pacemakers and tonic neurons—within the preBötC, and (2) possible functional roles of inhibitory neurons within the preBötC in rhythm generation. Obtained results indicate that (1) synaptic distribution within excitatory subnetwork of the evolved model network illustrates skewed/heavy-tailed degree distribution, and (2) inhibitory subnetwork influences excitatory subnetwork primarily through non-tonic pacemaker inhibitory neurons. Further, since small-world (SW) network is generally associated with network synchronization phenomena and is suggested as a possible network structure within the preBötC, we compared the performance of SW network with that of the evolved model network. Results show that evolved network is better than SW network at exhibiting synchronous bursts.
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Affiliation(s)
- Amit Lal
- Department of Biomedical Engineering, Peking University, Beijing, 100871 P. R. China
| | - Yoshitaka Oku
- Department of Physiology, Hyogo College of Medicine, Nishinomiya, 663-8501 Japan
- * E-mail:
| | - Hiroshi Someya
- School of Information Science and Technology, Tokai University, Hiratsuka, 259-1292 Japan
| | - Fumikazu Miwakeichi
- Department of Statistical Modeling, The Institute of Statistical Mathematics, Tachikawa, 190-8562 Japan
- Department of Statistical Science, School of Multidisciplinary Sciences, The Graduate University for Advanced Studies, Tachikawa, 190-8562, Japan
| | - Yoshiyasu Tamura
- Department of Statistical Modeling, The Institute of Statistical Mathematics, Tachikawa, 190-8562 Japan
- Department of Statistical Science, School of Multidisciplinary Sciences, The Graduate University for Advanced Studies, Tachikawa, 190-8562, Japan
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11
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Ocker GK, Litwin-Kumar A, Doiron B. Self-Organization of Microcircuits in Networks of Spiking Neurons with Plastic Synapses. PLoS Comput Biol 2015; 11:e1004458. [PMID: 26291697 PMCID: PMC4546203 DOI: 10.1371/journal.pcbi.1004458] [Citation(s) in RCA: 54] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2014] [Accepted: 07/19/2015] [Indexed: 11/18/2022] Open
Abstract
The synaptic connectivity of cortical networks features an overrepresentation of certain wiring motifs compared to simple random-network models. This structure is shaped, in part, by synaptic plasticity that promotes or suppresses connections between neurons depending on their joint spiking activity. Frequently, theoretical studies focus on how feedforward inputs drive plasticity to create this network structure. We study the complementary scenario of self-organized structure in a recurrent network, with spike timing-dependent plasticity driven by spontaneous dynamics. We develop a self-consistent theory for the evolution of network structure by combining fast spiking covariance with a slow evolution of synaptic weights. Through a finite-size expansion of network dynamics we obtain a low-dimensional set of nonlinear differential equations for the evolution of two-synapse connectivity motifs. With this theory in hand, we explore how the form of the plasticity rule drives the evolution of microcircuits in cortical networks. When potentiation and depression are in approximate balance, synaptic dynamics depend on weighted divergent, convergent, and chain motifs. For additive, Hebbian STDP these motif interactions create instabilities in synaptic dynamics that either promote or suppress the initial network structure. Our work provides a consistent theoretical framework for studying how spiking activity in recurrent networks interacts with synaptic plasticity to determine network structure.
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Affiliation(s)
- Gabriel Koch Ocker
- Department of Neuroscience, University of Pittsburgh, Pittsburgh, Pennsylvania, United States of America
- Center for the Neural Basis of Cognition, University of Pittsburgh and Carnegie Melon University, Pittsburgh, Pennsylvania, United States of America
| | - Ashok Litwin-Kumar
- Center for the Neural Basis of Cognition, University of Pittsburgh and Carnegie Melon University, Pittsburgh, Pennsylvania, United States of America
- Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania, United States of America
- Center for Theoretical Neuroscience, Columbia University, New York, New York, United States of America
| | - Brent Doiron
- Center for the Neural Basis of Cognition, University of Pittsburgh and Carnegie Melon University, Pittsburgh, Pennsylvania, United States of America
- Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania, United States of America
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12
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Regulation of burstiness by network-driven activation. Sci Rep 2015; 5:9714. [PMID: 25969428 PMCID: PMC4429350 DOI: 10.1038/srep09714] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2015] [Accepted: 03/13/2015] [Indexed: 01/12/2023] Open
Abstract
We prove that complex networks of interactions have the capacity to regulate and buffer unpredictable fluctuations in production events. We show that non-bursty network-driven activation dynamics can effectively regulate the level of burstiness in the production of nodes, which can be enhanced or reduced. Burstiness can be induced even when the endogenous inter-event time distribution of nodes' production is non-bursty. We find that hubs tend to be less susceptible to the networked regulatory effects than low degree nodes. Our results have important implications for the analysis and engineering of bursty activity in a range of systems, from communication networks to transcription and translation of genes into proteins in cells.
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13
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Luccioli S, Ben-Jacob E, Barzilai A, Bonifazi P, Torcini A. Clique of functional hubs orchestrates population bursts in developmentally regulated neural networks. PLoS Comput Biol 2014; 10:e1003823. [PMID: 25255443 PMCID: PMC4177675 DOI: 10.1371/journal.pcbi.1003823] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2014] [Accepted: 07/24/2014] [Indexed: 12/18/2022] Open
Abstract
It has recently been discovered that single neuron stimulation can impact network dynamics in immature and adult neuronal circuits. Here we report a novel mechanism which can explain in neuronal circuits, at an early stage of development, the peculiar role played by a few specific neurons in promoting/arresting the population activity. For this purpose, we consider a standard neuronal network model, with short-term synaptic plasticity, whose population activity is characterized by bursting behavior. The addition of developmentally inspired constraints and correlations in the distribution of the neuronal connectivities and excitabilities leads to the emergence of functional hub neurons, whose stimulation/deletion is critical for the network activity. Functional hubs form a clique, where a precise sequential activation of the neurons is essential to ignite collective events without any need for a specific topological architecture. Unsupervised time-lagged firings of supra-threshold cells, in connection with coordinated entrainments of near-threshold neurons, are the key ingredients to orchestrate population activity. To which extent a single neuron can influence brain circuits/networks dynamics? Why only a few neurons display such a strong power? These open questions are inspired by recent experimental observations in developing and adult neuronal circuits, as well as by classical debates within the framework of the single neuron doctrine. In this work we identify and present a mechanism which can explain in neuronal circuits, at some early stage of their development, how and why only a few specific neurons can exhibit such power. For this purpose, we consider a standard neuronal network model whose population activity is characterized by bursting behavior. The introduction of a distribution of correlated neuronal excitabilities and degrees, inspired by the simultaneous presence of younger and older neurons in the network, leads to the emergence of functional hub neurons. These critical cells, whenever perturbed, are capable of suppressing network synchronization. Notably, we show that their strong influence on the population dynamics is not related to their structural properties, but to their operational and structural integration into a clique. These results highlight how network-wide effects can be induced by single neurons without any need for a specific topological architecture.
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Affiliation(s)
- Stefano Luccioli
- Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, Sesto Fiorentino, Italy
- Joint Italian-Israeli Laboratory on Integrative Network Neuroscience, Tel Aviv University, Ramat Aviv, Israel
- * E-mail: (SL); (PB)
| | - Eshel Ben-Jacob
- Joint Italian-Israeli Laboratory on Integrative Network Neuroscience, Tel Aviv University, Ramat Aviv, Israel
- Beverly and Sackler Faculty of Exact Sciences School of Physics and Astronomy, Tel Aviv University, Ramat Aviv, Israel
| | - Ari Barzilai
- Joint Italian-Israeli Laboratory on Integrative Network Neuroscience, Tel Aviv University, Ramat Aviv, Israel
- Department of Neurobiology, George S. Wise Faculty of Life Sciences and Sagol School of Neuroscience, Tel Aviv University, Ramat Aviv, Israel
| | - Paolo Bonifazi
- Joint Italian-Israeli Laboratory on Integrative Network Neuroscience, Tel Aviv University, Ramat Aviv, Israel
- Beverly and Sackler Faculty of Exact Sciences School of Physics and Astronomy, Tel Aviv University, Ramat Aviv, Israel
- Department of Neurobiology, George S. Wise Faculty of Life Sciences and Sagol School of Neuroscience, Tel Aviv University, Ramat Aviv, Israel
- * E-mail: (SL); (PB)
| | - Alessandro Torcini
- Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, Sesto Fiorentino, Italy
- Joint Italian-Israeli Laboratory on Integrative Network Neuroscience, Tel Aviv University, Ramat Aviv, Israel
- INFN - Sezione di Firenze and CSDC, Sesto Fiorentino, Italy
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14
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Nieto-Posadas A, Flores-Martínez E, Lorea-Hernández JJ, Rivera-Angulo AJ, Pérez-Ortega JE, Bargas J, Peña-Ortega F. Change in network connectivity during fictive-gasping generation in hypoxia: prevention by a metabolic intermediate. Front Physiol 2014; 5:265. [PMID: 25101002 PMCID: PMC4107943 DOI: 10.3389/fphys.2014.00265] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2014] [Accepted: 06/25/2014] [Indexed: 11/13/2022] Open
Abstract
The neuronal circuit in charge of generating the respiratory rhythms, localized in the pre-Bötzinger complex (preBötC), is configured to produce fictive-eupnea during normoxia and reconfigures to produce fictive-gasping during hypoxic conditions in vitro. The mechanisms involved in such reconfiguration have been extensively investigated by cell-focused studies, but the actual changes at the network level remain elusive. Since a failure to generate gasping has been linked to Sudden Infant Death Syndrome (SIDS), the study of gasping generation and pharmacological approaches to promote it may have clinical relevance. Here, we study the changes in network dynamics and circuit reconfiguration that occur during the transition to fictive-gasping generation in the brainstem slice preparation by recording the preBötC with multi-electrode arrays and assessing correlated firing among respiratory neurons or clusters of respiratory neurons (multiunits). We studied whether the respiratory network reconfiguration in hypoxia involves changes in either the number of active respiratory elements, the number of functional connections among elements, or the strength of these connections. Moreover, we tested the influence of isocitrate, a Krebs cycle intermediate that has recently been shown to promote breathing, on the configuration of the preBötC circuit during normoxia and on its reconfiguration during hypoxia. We found that, in contrast to previous suggestions based on cell-focused studies, the number and the overall activity of respiratory neurons change only slightly during hypoxia. However, hypoxia induces a reduction in the strength of functional connectivity within the circuit without reducing the number of connections. Isocitrate prevented this reduction during hypoxia while increasing the strength of network connectivity. In conclusion, we provide an overview of the configuration of the respiratory network under control conditions and how it is reconfigured during fictive-gasping. Additionally, our data support the use of isocitrate to favor respiratory rhythm generation under normoxia and to prevent some of the changes in the respiratory network under hypoxic conditions.
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Affiliation(s)
- Andrés Nieto-Posadas
- Departamento de Neurobiología del Desarrollo y Neurofisiología, Instituto de Neurobiología, Universidad Nacional Autónoma de México Querétaro, México
| | - Ernesto Flores-Martínez
- Departamento de Neurobiología del Desarrollo y Neurofisiología, Instituto de Neurobiología, Universidad Nacional Autónoma de México Querétaro, México
| | - Jonathan-Julio Lorea-Hernández
- Departamento de Neurobiología del Desarrollo y Neurofisiología, Instituto de Neurobiología, Universidad Nacional Autónoma de México Querétaro, México
| | - Ana-Julia Rivera-Angulo
- Departamento de Neurobiología del Desarrollo y Neurofisiología, Instituto de Neurobiología, Universidad Nacional Autónoma de México Querétaro, México
| | - Jesús-Esteban Pérez-Ortega
- División de Neurociencias, Instituto de Fisiología Celular, Universidad Nacional Autónoma de México México D.F., México
| | - José Bargas
- División de Neurociencias, Instituto de Fisiología Celular, Universidad Nacional Autónoma de México México D.F., México
| | - Fernando Peña-Ortega
- Departamento de Neurobiología del Desarrollo y Neurofisiología, Instituto de Neurobiología, Universidad Nacional Autónoma de México Querétaro, México
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15
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Klinshov VV, Teramae JN, Nekorkin VI, Fukai T. Dense neuron clustering explains connectivity statistics in cortical microcircuits. PLoS One 2014; 9:e94292. [PMID: 24732632 PMCID: PMC3986068 DOI: 10.1371/journal.pone.0094292] [Citation(s) in RCA: 40] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2013] [Accepted: 03/14/2014] [Indexed: 11/17/2022] Open
Abstract
Local cortical circuits appear highly non-random, but the underlying connectivity rule remains elusive. Here, we analyze experimental data observed in layer 5 of rat neocortex and suggest a model for connectivity from which emerge essential observed non-random features of both wiring and weighting. These features include lognormal distributions of synaptic connection strength, anatomical clustering, and strong correlations between clustering and connection strength. Our model predicts that cortical microcircuits contain large groups of densely connected neurons which we call clusters. We show that such a cluster contains about one fifth of all excitatory neurons of a circuit which are very densely connected with stronger than average synapses. We demonstrate that such clustering plays an important role in the network dynamics, namely, it creates bistable neural spiking in small cortical circuits. Furthermore, introducing local clustering in large-scale networks leads to the emergence of various patterns of persistent local activity in an ongoing network activity. Thus, our results may bridge a gap between anatomical structure and persistent activity observed during working memory and other cognitive processes.
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Affiliation(s)
- Vladimir V Klinshov
- Nonlinear Dynamics Department, Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia; Laboratory for Neural Circuit Theory, RIKEN Brain Science Institute, Wako, Saitama, Japan; Laboratory for Nonlinear Oscillatory-Wave Physics, University of Nizhni Novgorod, Nizhni Novgorod, Russia
| | - Jun-nosuke Teramae
- Laboratory for Neural Circuit Theory, RIKEN Brain Science Institute, Wako, Saitama, Japan; Department of Bioinformatic Engineering, Osaka University, Suita, Osaka, Japan; PRESTO, Japan Science and Technology Agency, Kawaguchi, Saitama, Japan
| | - Vladimir I Nekorkin
- Nonlinear Dynamics Department, Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia; Laboratory for Nonlinear Oscillatory-Wave Physics, University of Nizhni Novgorod, Nizhni Novgorod, Russia; Department of Oscillations Theory and Automatic Control, University of Nizhni Novgorod, Nizhni Novgorod, Russia
| | - Tomoki Fukai
- Laboratory for Neural Circuit Theory, RIKEN Brain Science Institute, Wako, Saitama, Japan; CREST, Japan Science and Technology Agency, Kawaguchi, Saitama, Japan
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16
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van Ooyen A, Carnell A, de Ridder S, Tarigan B, Mansvelder HD, Bijma F, de Gunst M, van Pelt J. Independently outgrowing neurons and geometry-based synapse formation produce networks with realistic synaptic connectivity. PLoS One 2014; 9:e85858. [PMID: 24454938 PMCID: PMC3894200 DOI: 10.1371/journal.pone.0085858] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2013] [Accepted: 12/03/2013] [Indexed: 11/18/2022] Open
Abstract
Neuronal signal integration and information processing in cortical networks critically depend on the organization of synaptic connectivity. During development, neurons can form synaptic connections when their axonal and dendritic arborizations come within close proximity of each other. Although many signaling cues are thought to be involved in guiding neuronal extensions, the extent to which accidental appositions between axons and dendrites can already account for synaptic connectivity remains unclear. To investigate this, we generated a local network of cortical L2/3 neurons that grew out independently of each other and that were not guided by any extracellular cues. Synapses were formed when axonal and dendritic branches came by chance within a threshold distance of each other. Despite the absence of guidance cues, we found that the emerging synaptic connectivity showed a good agreement with available experimental data on spatial locations of synapses on dendrites and axons, number of synapses by which neurons are connected, connection probability between neurons, distance between connected neurons, and pattern of synaptic connectivity. The connectivity pattern had a small-world topology but was not scale free. Together, our results suggest that baseline synaptic connectivity in local cortical circuits may largely result from accidentally overlapping axonal and dendritic branches of independently outgrowing neurons.
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Affiliation(s)
- Arjen van Ooyen
- Department of Integrative Neurophysiology, Center for Neurogenomics and Cognitive Research, VU University Amsterdam, Amsterdam, The Netherlands
| | - Andrew Carnell
- Department of Integrative Neurophysiology, Center for Neurogenomics and Cognitive Research, VU University Amsterdam, Amsterdam, The Netherlands
| | - Sander de Ridder
- Department of Integrative Neurophysiology, Center for Neurogenomics and Cognitive Research, VU University Amsterdam, Amsterdam, The Netherlands
| | - Bernadetta Tarigan
- Department of Mathematics, VU University Amsterdam, Amsterdam, The Netherlands
| | - Huibert D. Mansvelder
- Department of Integrative Neurophysiology, Center for Neurogenomics and Cognitive Research, VU University Amsterdam, Amsterdam, The Netherlands
| | - Fetsje Bijma
- Department of Mathematics, VU University Amsterdam, Amsterdam, The Netherlands
| | - Mathisca de Gunst
- Department of Mathematics, VU University Amsterdam, Amsterdam, The Netherlands
| | - Jaap van Pelt
- Department of Integrative Neurophysiology, Center for Neurogenomics and Cognitive Research, VU University Amsterdam, Amsterdam, The Netherlands
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17
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Mäki-Marttunen T, Aćimović J, Ruohonen K, Linne ML. Structure-dynamics relationships in bursting neuronal networks revealed using a prediction framework. PLoS One 2013; 8:e69373. [PMID: 23935998 PMCID: PMC3723901 DOI: 10.1371/journal.pone.0069373] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2013] [Accepted: 06/07/2013] [Indexed: 11/25/2022] Open
Abstract
The question of how the structure of a neuronal network affects its functionality has gained a lot of attention in neuroscience. However, the vast majority of the studies on structure-dynamics relationships consider few types of network structures and assess limited numbers of structural measures. In this in silico study, we employ a wide diversity of network topologies and search among many possibilities the aspects of structure that have the greatest effect on the network excitability. The network activity is simulated using two point-neuron models, where the neurons are activated by noisy fluctuation of the membrane potential and their connections are described by chemical synapse models, and statistics on the number and quality of the emergent network bursts are collected for each network type. We apply a prediction framework to the obtained data in order to find out the most relevant aspects of network structure. In this framework, predictors that use different sets of graph-theoretic measures are trained to estimate the activity properties, such as burst count or burst length, of the networks. The performances of these predictors are compared with each other. We show that the best performance in prediction of activity properties for networks with sharp in-degree distribution is obtained when the prediction is based on clustering coefficient. By contrast, for networks with broad in-degree distribution, the maximum eigenvalue of the connectivity graph gives the most accurate prediction. The results shown for small () networks hold with few exceptions when different neuron models, different choices of neuron population and different average degrees are applied. We confirm our conclusions using larger () networks as well. Our findings reveal the relevance of different aspects of network structure from the viewpoint of network excitability, and our integrative method could serve as a general framework for structure-dynamics studies in biosciences.
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Affiliation(s)
- Tuomo Mäki-Marttunen
- Department of Signal Processing, Tampere University of Technology, Tampere, Finland.
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18
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Lindsey BG, Rybak IA, Smith JC. Computational models and emergent properties of respiratory neural networks. Compr Physiol 2012; 2:1619-70. [PMID: 23687564 PMCID: PMC3656479 DOI: 10.1002/cphy.c110016] [Citation(s) in RCA: 62] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
Computational models of the neural control system for breathing in mammals provide a theoretical and computational framework bringing together experimental data obtained from different animal preparations under various experimental conditions. Many of these models were developed in parallel and iteratively with experimental studies and provided predictions guiding new experiments. This data-driven modeling approach has advanced our understanding of respiratory network architecture and neural mechanisms underlying generation of the respiratory rhythm and pattern, including their functional reorganization under different physiological conditions. Models reviewed here vary in neurobiological details and computational complexity and span multiple spatiotemporal scales of respiratory control mechanisms. Recent models describe interacting populations of respiratory neurons spatially distributed within the Bötzinger and pre-Bötzinger complexes and rostral ventrolateral medulla that contain core circuits of the respiratory central pattern generator (CPG). Network interactions within these circuits along with intrinsic rhythmogenic properties of neurons form a hierarchy of multiple rhythm generation mechanisms. The functional expression of these mechanisms is controlled by input drives from other brainstem components,including the retrotrapezoid nucleus and pons, which regulate the dynamic behavior of the core circuitry. The emerging view is that the brainstem respiratory network has rhythmogenic capabilities at multiple levels of circuit organization. This allows flexible, state-dependent expression of different neural pattern-generation mechanisms under various physiological conditions,enabling a wide repertoire of respiratory behaviors. Some models consider control of the respiratory CPG by pulmonary feedback and network reconfiguration during defensive behaviors such as cough. Future directions in modeling of the respiratory CPG are considered.
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Affiliation(s)
- Bruce G Lindsey
- Department of Molecular Pharmacology and Physiology and Neuroscience Program, University of South Florida College of Medicine, Tampa, Florida, USA.
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19
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Lamb DG, Calabrese RL. Small is beautiful: models of small neuronal networks. Curr Opin Neurobiol 2012; 22:670-5. [PMID: 22364687 DOI: 10.1016/j.conb.2012.01.010] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2012] [Revised: 01/23/2012] [Accepted: 01/24/2012] [Indexed: 01/23/2023]
Abstract
Modeling has contributed a great deal to our understanding of how individual neurons and neuronal networks function. In this review, we focus on models of the small neuronal networks of invertebrates, especially rhythmically active CPG networks. Models have elucidated many aspects of these networks, from identifying key interacting membrane properties to pointing out gaps in our understanding, for example missing neurons. Even the complex CPGs of vertebrates, such as those that underlie respiration, have been reduced to small network models to great effect. Modeling of these networks spans from simplified models, which are amenable to mathematical analyses, to very complicated biophysical models. Some researchers have now adopted a population approach, where they generate and analyze many related models that differ in a few to several judiciously chosen free parameters; often these parameters show variability across animals and thus justify the approach. Models of small neuronal networks will continue to expand and refine our understanding of how neuronal networks in all animals program motor output, process sensory information and learn.
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Affiliation(s)
- Damon G Lamb
- Emory University, Department of Biology, Atlanta, GA 30322, United States
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20
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McDonnell MD, Mohan A, Stricker C, Ward LM. Input-rate modulation of γ oscillations is sensitive to network topology, delays and short-term plasticity. Brain Res 2011; 1434:162-77. [PMID: 22000590 DOI: 10.1016/j.brainres.2011.08.070] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2011] [Revised: 08/29/2011] [Accepted: 08/30/2011] [Indexed: 11/24/2022]
Abstract
Simulated networks of excitatory and inhibitory neurons have previously been shown to reproduce critical features of experimental data regarding neural coding in V1, such as a positive relationship between thalamic input spike rate and the power of gamma frequency oscillations. This effect, referred to as modulated gamma power, could represent a neural code in V1 for stimulus characteristics that affect thalamic spike rate such as contrast or intensity. The simulated network's assumptions included homogeneous random connectivity, equal synaptic delays after spike arrival, and constant synaptic efficacies. Plausible alternative assumptions include small world connectivity, a wide distribution of axonal propagation delays, and short term synaptic plasticity, and here we assess the individual impact of each of these on the model's success in reproducing modulated gamma power. First, we developed several alternative algorithms for simulating directed networks with clustered connectivity and balanced excitation and inhibition. We found that modulated gamma power was absent in all small-world networks that had a relatively low abundance of reciprocal connectivity, which suggests that such motifs are present in V1 cortical networks at levels at least equal to those found in random networks. We also found in a different network type that the balance of excitation and inhibition could be destroyed when the network was in the small-world regime. Given all neurons had identical in-degrees, this result suggests that balance relies on motif distributions as well as mean connectivity. Second, altering the distribution of axonal delays had little effect, but increasing the mean delay led to a secondary gamma modulation at harmonics of the main peak, and since this is not observed experimentally, it suggests a mean delay in V1 networks less than 2 ms. Finally, we compared two types of excitatory synaptic plasticity, and found that modulated beta power emerged in addition to gamma power for one type, in the presence of short term depression in interneurons. This article is part of a Special Issue entitled "Neural Coding".
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Affiliation(s)
- Mark D McDonnell
- Computational & Theoretical Neuroscience Laboratory, Institute for Telecommunications Research, University of South Australia, Mawson Lakes, SA 5095, Australia.
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21
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Hermundstad AM, Brown KS, Bassett DS, Carlson JM. Learning, memory, and the role of neural network architecture. PLoS Comput Biol 2011; 7:e1002063. [PMID: 21738455 PMCID: PMC3127797 DOI: 10.1371/journal.pcbi.1002063] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2010] [Accepted: 04/06/2011] [Indexed: 11/18/2022] Open
Abstract
The performance of information processing systems, from artificial neural networks to natural neuronal ensembles, depends heavily on the underlying system architecture. In this study, we compare the performance of parallel and layered network architectures during sequential tasks that require both acquisition and retention of information, thereby identifying tradeoffs between learning and memory processes. During the task of supervised, sequential function approximation, networks produce and adapt representations of external information. Performance is evaluated by statistically analyzing the error in these representations while varying the initial network state, the structure of the external information, and the time given to learn the information. We link performance to complexity in network architecture by characterizing local error landscape curvature. We find that variations in error landscape structure give rise to tradeoffs in performance; these include the ability of the network to maximize accuracy versus minimize inaccuracy and produce specific versus generalizable representations of information. Parallel networks generate smooth error landscapes with deep, narrow minima, enabling them to find highly specific representations given sufficient time. While accurate, however, these representations are difficult to generalize. In contrast, layered networks generate rough error landscapes with a variety of local minima, allowing them to quickly find coarse representations. Although less accurate, these representations are easily adaptable. The presence of measurable performance tradeoffs in both layered and parallel networks has implications for understanding the behavior of a wide variety of natural and artificial learning systems. Information processing systems, such as natural biological networks and artificial computational networks, exhibit a strong interdependence between structural organization and functional performance. However, the extent to which variations in structure impact performance is not well understood, particularly in systems whose functionality must be simultaneously flexible and stable. By statistically analyzing the behavior of network systems during flexible learning and stable memory processes, we quantify the impact of structural variations on the ability of the network to learn, modify, and retain representations of information. Across a range of architectures drawn from both natural and artificial systems, we show that these networks face tradeoffs between the ability to learn and retain information, and the observed behavior varies depending on the initial network state and the time given to process information. Furthermore, we analyze the difficulty with which different network architectures produce accurate versus generalizable representations of information, thereby identifying the structural mechanisms that give rise to functional tradeoffs between learning and memory.
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Affiliation(s)
- Ann M Hermundstad
- Physics Department, University of California, Santa Barbara, Santa Barbara, California, United States of America.
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