相关论文

Fast Global Oscillations in Networks of Integrate-and-Fire Neurons with Low Firing Rates

Abstract:We study analytically the dynamics of a network of sparsely connected inhibitory integrate-and-fire neurons in a regime where individual neurons emit spikes irregularly and at a low rate. In the limit when the number of neurons N , the network exhibits a sharp transition between a stationary and an oscillatory global activity regime where neurons are weakly synchronized. The activity becomes oscillatory when the inhibitory feedback is strong enough. The period of the global oscillation is found to be mainly controlled by synaptic times but depends also on the characteristics of the external input. In large but finite networks, the analysis shows that global oscillations of finite coherence time generically exist both above and below the critical inhibition threshold. Their characteristics are determined as functions of systems parameters in these two different regimes. The results are found to be in good agreement with numerical simulations.

参考文献

[1]  G. Laurent,et al.  Encoding of Olfactory Information with Oscillating Neural Assemblies , 1994, Science.

[2]  Terrence J. Sejnowski,et al.  RAPID STATE SWITCHING IN BALANCED CORTICAL NETWORK MODELS , 1995 .

[3]  M. Hirsch,et al.  Differential Equations, Dynamical Systems, and Linear Algebra , 1974 .

[4]  R. Traub,et al.  Synchronized oscillations in interneuron networks driven by metabotropic glutamate receptor activation , 1995, Nature.

[5]  C. Gray,et al.  Chattering Cells: Superficial Pyramidal Neurons Contributing to the Generation of Synchronous Oscillations in the Visual Cortex , 1996, Science.

[6]  Theo. B. Hyslop,et al.  Anatomy of cortex. , 2022 .

[7]  G. Buzsáki,et al.  Sharp wave-associated high-frequency oscillation (200 Hz) in the intact hippocampus: network and intracellular mechanisms , 1995, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[8]  R. Eckhorn,et al.  High frequency (60-90 Hz) oscillations in primary visual cortex of awake monkey. , 1993, Neuroreport.

[9]  S. Orszag,et al.  Advanced Mathematical Methods For Scientists And Engineers , 1979 .

[10]  Prof. Dr. Valentino Braitenberg,et al.  Anatomy of the Cortex , 1991, Studies of Brain Function.

[11]  J. Csicsvari,et al.  Reliability and State Dependence of Pyramidal Cell–Interneuron Synapses in the Hippocampus an Ensemble Approach in the Behaving Rat , 1998, Neuron.

[12]  G. Buzsáki,et al.  Gamma (40-100 Hz) oscillation in the hippocampus of the behaving rat , 1995, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[13]  W Singer,et al.  Visual feature integration and the temporal correlation hypothesis. , 1995, Annual review of neuroscience.

[14]  T. Sejnowski,et al.  Synchronous oscillatory activity in sensory systems: new vistas on mechanisms , 1997, Current Opinion in Neurobiology.

[15]  H. Sompolinsky,et al.  Chaos in Neuronal Networks with Balanced Excitatory and Inhibitory Activity , 1996, Science.

[16]  G. Buzsáki,et al.  High-frequency network oscillation in the hippocampus. , 1992, Science.

[17]  A. Treves Mean-field analysis of neuronal spike dynamics , 1993 .

[18]  Germán Mato,et al.  Synchrony in Excitatory Neural Networks , 1995, Neural Computation.

[19]  Nicolas Brunel,et al.  Dynamics of a recurrent network of spiking neurons before and following learning , 1997 .

[20]  D. Amit,et al.  Model of global spontaneous activity and local structured activity during delay periods in the cerebral cortex. , 1997, Cerebral cortex.

[21]  D. Kleinfeld,et al.  Visual stimuli induce waves of electrical activity in turtle cortex. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[22]  G. Laurent,et al.  Distinct Mechanisms for Synchronization and Temporal Patterning of Odor-Encoding Neural Assemblies , 1996, Science.

[23]  D. Kleinfeld,et al.  Waves and stimulus-modulated dynamics in an oscillating olfactory network. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[24]  Vreeswijk,et al.  Partial synchronization in populations of pulse-coupled oscillators. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[25]  Abbott,et al.  Asynchronous states in networks of pulse-coupled oscillators. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[26]  Shigeru Shinomoto,et al.  Phase Transitions and Their Bifurcation Analysis in a Large Population of Active Rotators with Mean-Field Coupling , 1988 .

[27]  Karma,et al.  Noise-Induced Coherence in Neural Networks. , 1996, Physical review letters.

[28]  W. Singer,et al.  Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties , 1989, Nature.

[29]  O. Paulsen,et al.  Cholinergic induction of network oscillations at 40 Hz in the hippocampus in vitro , 1998, Nature.

[30]  G. Buzsáki,et al.  Analysis of gamma rhythms in the rat hippocampus in vitro and in vivo. , 1996, The Journal of physiology.

[31]  G. Buzsáki,et al.  Temporal structure in spatially organized neuronal ensembles: a role for interneuronal networks , 1995, Current Opinion in Neurobiology.

[32]  S. Strogatz,et al.  Synchronization of pulse-coupled biological oscillators , 1990 .

[33]  Wulfram Gerstner,et al.  What Matters in Neuronal Locking? , 1996, Neural Computation.

[34]  C. E. Adams Tables of mathematical functions , 2022 .

[35]  N. Kopell,et al.  Rhythmogenesis, amplitude modulation, and multiplexing in a cortical architecture. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[36]  J. Rinzel,et al.  Emergent spindle oscillations and intermittent burst firing in a thalamic model: specific neuronal mechanisms. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[37]  W. Singer,et al.  Stimulus-dependent synchronization of neuronal responses in the visual cortex of the awake macaque monkey , 1996, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[38]  G. Laurent,et al.  Impaired odour discrimination on desynchronization of odour-encoding neural assemblies , 1997, Nature.

[39]  S. Strogatz,et al.  Stability of incoherence in a population of coupled oscillators , 1991 .

[40]  H. Davis Tables of mathematical functions , 1965 .

[41]  C. Gardiner Handbook of Stochastic Methods , 1983 .

[42]  W. Gerstner,et al.  Time structure of the activity in neural network models. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[43]  J. Rinzel,et al.  Clustering in globally coupled inhibitory neurons , 1994 .

[44]  R. Traub,et al.  Model of the origin of rhythmic population oscillations in the hippocampal slice. , 1989, Science.

[45]  G. Buzsáki,et al.  Gamma Oscillation by Synaptic Inhibition in a Hippocampal Interneuronal Network Model , 1996, The Journal of Neuroscience.

[46]  S. Chandrasekhar Stochastic problems in Physics and Astronomy , 1943 .

引用
Spike statistics and coding properties of phase models
2013
Interneuron subtypes and orientation tuning
Nature
2014
Discharges Network Oscillations With Irregular Neuronal Contributions of Intrinsic Membrane Dynamics to
2005
Cellular / Molecular Neuronal Morphology Generates High-Frequency Firing Resonance
2015
A stochastic mean field model for an excitatory and inhibitory synaptic drive cortical neuronal network
2012 IEEE 51st IEEE Conference on Decision and Control (CDC)
2012
A stochastic mean field model for an excitatory and inhibitory synaptic drive cortical neuronal network
CDC
2012
Supervised learning in spiking neural networks with noise-threshold
Neurocomputing
2017
GPUs Outperform Current HPC and Neuromorphic Solutions in Terms of Speed and Energy When Simulating a Highly-Connected Cortical Model
Front. Neurosci.
2018
Codes and Goals of Neuronal Representations
2003
What determines the frequency of fast network oscillations with irregular neural discharges? I. Synaptic dynamics and excitation-inhibition balance.
Journal of neurophysiology
2003
Coding properties of spiking neurons: reverse and cross-correlations
Neural Networks
2001
How well do mean field theories of spiking quadratic-integrate-and-fire networks work in realistic parameter regimes?
Journal of Computational Neuroscience
2013
Stochastic resonance in Hodgkin-Huxley neuron induced by unreliable synaptic transmission.
Journal of theoretical biology
2012
Spatiotemporal dynamics of continuum neural fields
2012
A DISTRIBUTION OF SPIKE TRANSMISSION DELAYS AFFECTS THE STABILITY OF INTERACTING SPIKING NEURONS
2003
Delayed feedback control of collective synchrony: an approach to suppression of pathological brain rhythms.
Physical review. E, Statistical, nonlinear, and soft matter physics
2004
Synchrony in stochastically driven neuronal networks with complex topologies.
Physical review. E, Statistical, nonlinear, and soft matter physics
2015
Impact of intrinsic biophysical diversity on the activity of spiking neurons
1208.5350
2012
Role of delays in shaping spatiotemporal dynamics of neuronal activity in large networks.
Physical review letters
2005
STDP-driven networks and the C. elegans neuronal network
1004.5060
2010