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Synchronization of strongly coupled excitatory neurons: relating network behavior to biophysics

Corey D Acker, Nancy Kopell, John A White
Journal of Computational Neuroscience  
Behavior of a network of neurons is closely tied to the properties of the individual neurons. We study this relationship in models of layer II stellate cells (SCs) of the medial entorhinal cortex.  ...  We apply "spike time response" (STR) methods, in which the effects of synaptic perturbations on the timing of subsequent spikes are used to predict how these neurons may synchronize at theta frequencies  ...  This work was supported by grants from the National Institutes of Health and National Science Foundation (MH 047150 and NSF DMS-9706694 to NK, NS34425 to JAW, and DMS-0109427 to the Center for BioDynamics  ... 
pmid:12843696 fatcat:rarn4d6hvvcfba2cawzagxq3qu

Simple model of spiking neurons

E.M. Izhikevich
2003 IEEE Transactions on Neural Networks  
A model is presented that reproduces spiking and bursting behavior of known types of cortical neurons.  ...  Using this model, one can simulate tens of thousands of spiking cortical neurons in real time (1 ms resolution) using a desktop PC.  ...  Chen, who read the first draft of the manuscript and made a number of useful suggestions.  ... 
doi:10.1109/tnn.2003.820440 pmid:18244602 fatcat:43w4wy5ylffm3ehchwk7bub4k4

Neurons as oscillators

Klaus M. Stiefel, G. Bard Ermentrout
2016 Journal of Neurophysiology  
We further show that the response of a neuron to correlated inputs depends on the shape of the PRC. We then explain how the PRC of single neurons can be used to predict neural network behavior.  ...  Next, we show how the PRC can be related to a number of common measures used to quantify neuronal firing, such as the spike-triggered average and the peristimulus histogram.  ...  GRANTS This work was supported by National Science Foundation Grant DMS1219753 (to G. B. Ermentrout). DISCLOSURES No conflicts of interest, financial or otherwise, are declared by the authors.  ... 
doi:10.1152/jn.00525.2015 pmid:27683887 pmcid:PMC5192043 fatcat:bnbbxbj5t5hahcsulgl43gelom

Synaptic Plasticity and Spike Synchronisation in Neuronal Networks

Rafael R. Borges, Fernando S. Borges, Ewandson L. Lameu, Paulo R. Protachevicz, Kelly C. Iarosz, Iberê L. Caldas, Ricardo L. Viana, Elbert E. N. Macau, Murilo S. Baptista, Celso Grebogi, Antonio M. Batista
2017 Brazilian journal of physics  
Finally, we show how the synchronous behaviour of the evolved network will reflect its evolved topology.  ...  For initial networks with considerably larger inhibitory strengths, we observe the emergence of a complex evolved topology, where neurons sparsely connected to other neurons, also a typical topology of  ...  We show that the transition from weakly synchronous to strongly synchronous states depends on the neuronal network architecture, as well as to the STDP network evolves to non-trivial topology.  ... 
doi:10.1007/s13538-017-0529-5 fatcat:2pmzarrjpjeftomzqc3xplmkbm

Sparsely synchronized neuronal oscillations

Nicolas Brunel, Vincent Hakim
2008 Chaos  
We discuss here the properties of fast global oscillations that emerge in networks of neurons firing irregularly at a low rate.  ...  We first provide a simple introduction to these sparsely synchronized oscillations, then show how they can be studied analytically in the simple setting of rate models and leaky integrate-and-fire neurons  ...  EXCITATORY-INHIBITORY NETWORKS We have considered so far purely inhibitory networks. What happens when excitatory neurons are coupled to the network of inhibitory neurons?  ... 
doi:10.1063/1.2779858 pmid:18377094 fatcat:4iegzrk2kjcvdhxcvl4dhkf77a

Impact of Adaptation Currents on Synchronization of Coupled Exponential Integrate-and-Fire Neurons

Josef Ladenbauer, Moritz Augustin, LieJune Shiau, Klaus Obermayer, Olaf Sporns
2012 PLoS Computational Biology  
It is therefore important to determine which properties of neurons influence their collective behavior in a network and to understand how.  ...  Author summary: Synchronization of neuronal spiking in the brain is related to cognitive functions, such as perception, attention, and memory.  ...  Synchronization and clustering in aEIF networks In order to examine how the behavior of pairs of coupled phase neurons relates to networks of spiking neurons, we performed numerical simulations of networks  ... 
doi:10.1371/journal.pcbi.1002478 pmid:22511861 pmcid:PMC3325187 fatcat:z3ykaji5ezaztgsc62iogcheze

Pyramidal Neuron as Two-Layer Neural Network

Panayiota Poirazi, Terrence Brannon, Bartlett W. Mel
2003 Neuron  
and Mel, 2000; Poirazi et al., 2003 [this issue of Neuron]).  ...  to complex stimuli consisting of dozens of 2000), we found that when a total of 16 excitatory synhigh-frequency activated synapses distributed throughapses were placed on two identical cylindrical branches  ...  To do this, we ran a stimulus set with 50 excitatory ize the biophysical model's response behavior.  ... 
doi:10.1016/s0896-6273(03)00149-1 pmid:12670427 fatcat:nnlj6km7wbfgxcaupcariddbvm

Inhibitory transmission, activity-dependent ionic changes and neuronal network oscillations

P Jedlicka, K H Backus
2006 Physiological Research  
and influence the network behavior.  ...  In this review, we summarize general mechanisms of synchronous neuronal oscillations.  ...  shape the actual behavior of the neural network.  ... 
pmid:15910171 fatcat:7zmy42mapngxposbsagj2ewl5e

Continuum of weakly coupled oscillatory McKean neurons

M. Denman-Johnson, S. Coombes
2003 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
Here we use tools from coupled oscillator theory to study weakly coupled networks of McKean neurons.  ...  Using numerical techniques we show that the McKean system has traveling wave phase-locked solutions consistent with that of a network of more biophysically detailed Hodgkin-Huxley neurons.  ...  Interestingly, they show that synchrony can be stable for localized excitatory coupling, but long range excitatory coupling leads to an unstable synchronous state.  ... 
doi:10.1103/physreve.67.051903 pmid:12786174 fatcat:h5pbkfl4jnd7tk6eg3auy3hnge

Dynamics of Strongly Coupled Spiking Neurons

Paul C. Bressloff, S. Coombes
2000 Neural Computation  
First, a globally coupled network of identical neurons with strong inhibitory coupling is shown to exhibit oscillator death in which some of the neurons suppress the activity of others.  ...  The dynamics is compared with that of a corresponding network of analog neurons in which the outputs of the neurons are taken to be mean firing rates.  ...  We are also grateful for the constructive comments of the referees and the suggestion to include the example in section 4.6. The research was supported by grant number GR/K86220 from the EPSRC (UK).  ... 
doi:10.1162/089976600300015907 pmid:10636934 fatcat:6la2wwteq5ebtgvhv2rg7bg2eu

Neuronal Oscillations in Cortical Networks

G. Buzsaki
2004 Science  
Mammalian cortical neurons form behavior-dependent oscillating networks of various sizes, which span five orders of magnitude in frequency.  ...  Are neuronal oscillations an inevitable by-product, similar to bridge vibrations, or an essential part of the brain's design?  ...  The synchronous activity of oscillating networks is now viewed as the critical "middle ground" linking single-neuron activity to behavior (2) (3) (4) (5) (6) 15) .  ... 
doi:10.1126/science.1099745 pmid:15218136 fatcat:v3wfg3d5jrbfrp2pufyyrtwhxa

Synchronization in Hybrid Neuronal Networks of the Hippocampal Formation

Theoden I. Netoff, Matthew I. Banks, Alan D. Dorval, Corey D. Acker, Julie S. Haas, Nancy Kopell, John A. White
2005 Journal of Neurophysiology  
We then measured responses of free-running hybrid neuronal networks, consisting of biological neurons coupled (via dynamic clamp) to biological or virtual counterparts.  ...  synchronization behavior.  ...  The point of this exercise is to test the ability of the STRCs to predict synchronization behavior.  ... 
doi:10.1152/jn.00982.2004 pmid:15525802 fatcat:5gywk6tu5nbxzh6zaqowh4dvfq

Sparse Gamma Rhythms Arising through Clustering in Adapting Neuronal Networks

Zachary P. Kilpatrick, Bard Ermentrout, Boris S. Gutkin
2011 PLoS Computational Biology  
This is then used to predict the relationship between the number of clusters arising spontaneously in the network as it relates to the adaptation time constant.  ...  Excitatory neurons form several clusters that fire every few cycles of the fast oscillation.  ...  Acknowledgments We thank John Guckenheimer for a personal communication regarding analysis of the singularly perturbed system.  ... 
doi:10.1371/journal.pcbi.1002281 pmid:22125486 pmcid:PMC3219625 fatcat:4gbvaxij3vempd732tfbqqhbw4

Networks of neurons as dynamical systems: from geometry to biophysics

Nancy Kopell
1998 Quarterly of Applied Mathematics  
One task of the people who study it is to try to connect the "wetware" (neurons and networks of them) with behavior such as seeing, moving, and proving theorems.  ...  Though dynamical systems ideas are even more broadly useful, this talk focuses on rhythmic behavior in networks of neurons.  ...  (For related work on networks of spiking neurons see [39] , [40] .) Recently, D. Terman, A.  ... 
doi:10.1090/qam/1668734 fatcat:ltm7rcizfzaxvjrmq2mc6yjorq

Phase-locking in weakly heterogeneous neuronal networks

Carson C. Chow
1998 Physica D : Non-linear phenomena  
We consider a model of N neurons with all-to-all synaptic coupling where the heterogeneity is in the firing frequency or intrinsic drive of the neurons.  ...  In homogeneous networks, many different periodic phase-locked states are possible. Their stability depends on the dynamics of the neuron and the coupling.  ...  Acknowledgements I would like to thank N. Kopell for many clarifying discussions and for constructive critiques of the manuscript. I thank S. Epstein, B. Ermentrout, W. Gerstner, and J.  ... 
doi:10.1016/s0167-2789(98)00082-7 fatcat:3uleed7z3bhwhjonskyeovmbdi
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