Effects of Noisy Drive on Rhythms in Networks of Excitatory and Inhibitory Neurons

Synchronous rhythmic spiking in neuronal networks can be brought about by the interaction between E-cells and Icells (excitatory and inhibitory cells). The I-cells gate and synchronize the E-cells, and the E-cells drive and synchronize the I-cells. We refer to rhythms generated in this way as PING (pyramidal-interneuronal gamma) rhythms. The PING mechanism requires that the drive II to the I-cells be sufficiently low; the rhythm is lost when II gets too large. This can happen in at least two ways. In the first mechanism, the I-cells spike in synchrony, but get ahead of the E-cells, spiking without being prompted by the E-cells. We call this phase walkthrough of the I-cells. In the second mechanism, the I-cells fail to synchronize, and their activity leads to complete suppression of the E-cells. Noisy spiking in the E-cells, generated by noisy external drive, adds excitatory drive to the I-cells and may lead to phase walkthrough. Noisy spiking in the I-cells adds inhibition to the E-cells and may lead to suppression of the E-cells. An analysis of the conditions under which noise leads to phase walkthrough of the I-cells or suppression of the E-cells shows that PING rhythms at frequencies far below the gamma range are robust to noise only if network parameter values are tuned very carefully. Together with an argument explaining why the PING mechanism does not work far above the gamma range in the presence of heterogeneity, this justifies the G in PING.

[1]  Germán Mato,et al.  Asynchronous States and the Emergence of Synchrony in Large Networks of Interacting Excitatory and Inhibitory Neurons , 2003, Neural Computation.

[2]  B. Richmond,et al.  Intrinsic dynamics in neuronal networks. I. Theory. , 2000, Journal of neurophysiology.

[3]  Wulfram Gerstner,et al.  Population Dynamics of Spiking Neurons: Fast Transients, Asynchronous States, and Locking , 2000, Neural Computation.

[4]  S. Epstein,et al.  Background gamma rhythmicity and attention in cortical local circuits: a computational study. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[5]  W. Gerstner,et al.  Coherence and incoherence in a globally coupled ensemble of pulse-emitting units. , 1993, Physical review letters.

[6]  J F Storm,et al.  An after‐hyperpolarization of medium duration in rat hippocampal pyramidal cells. , 1989, The Journal of physiology.

[7]  van Vreeswijk C.  Analysis of the asynchronous state in networks of strongly coupled oscillators , 2000, Physical review letters.

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

[9]  M. Hasselmo.  Neuromodulation: acetylcholine and memory consolidation , 1999, Trends in Cognitive Sciences.

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

[11]  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.

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

[13]  Wolf Singer,et al.  Neuronal Synchrony: A Versatile Code for the Definition of Relations? , 1999, Neuron.

[14]  P. Schwartzkroin,et al.  Local circuit synaptic interactions in hippocampal brain slices , 1981, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[15]  Eve Marder,et al.  Mechanisms for oscillation and frequency control in reciprocally inhibitory model neural networks , 1994, Journal of Computational Neuroscience.

[16]  Boris S. Gutkin,et al.  Dynamics of Membrane Excitability Determine Interspike Interval Variability: A Link Between Spike Generation Mechanisms and Cortical Spike Train Statistics , 1998, Neural Computation.

[17]  Germán Mato,et al.  Synchrony in Heterogeneous Networks of Spiking Neurons , 2000, Neural Computation.

[18]  Carson C. Chow,et al.  Frequency Control in Synchronized Networks of Inhibitory Neurons , 1998, Journal of Computational Neuroscience.

[19]  G. Ermentrout,et al.  Chapter 1 - Mechanisms of Phase-Locking and Frequency Control in Pairs of Coupled Neural Oscillators* , 2002 .

[20]  N Kopell,et al.  Gap Junctions between Interneuron Dendrites Can Enhance Synchrony of Gamma Oscillations in Distributed Networks , 2001, The Journal of Neuroscience.

[21]  C. Vanvreeswijk.  Analysis of the asynchronous state in networks of strongly coupled oscillators , 2000 .

[22]  John Hart,et al.  Interactions between thalamic and cortical rhythms during semantic memory recall in human , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[23]  Xiao-Jing Wang,et al.  What determines the frequency of fast network oscillations with irregular neural discharges? I. Synaptic dynamics and excitation-inhibition balance. , 2003, Journal of neurophysiology.

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

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

[26]  W. Singer,et al.  Rapid feature selective neuronal synchronization through correlated latency shifting , 2001, Nature Neuroscience.

[27]  Nicolas Brunel,et al.  Phase diagrams of sparsely connected networks of excitatory and inhibitory spiking neurons , 2000, Neurocomputing.

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

[29]  Paul H. E. Tiesinga,et al.  Attentional modulation of firing rate and synchrony in a model cortical network , 2005, Journal of Computational Neuroscience.

[30]  W. Singer,et al.  Synchronization of oscillatory responses in visual cortex correlates with perception in interocular rivalry. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[31]  G B Ermentrout,et al.  Fine structure of neural spiking and synchronization in the presence of conduction delays. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[32]  Bard Ermentrout,et al.  When inhibition not excitation synchronizes neural firing , 1994, Journal of Computational Neuroscience.

[33]  Nancy Kopell,et al.  Synchronization of Strongly Coupled Excitatory Neurons: Relating Network Behavior to Biophysics , 2003, Journal of Computational Neuroscience.

[34]  Serge Charpak,et al.  Potassium conductances in hippocampal neurons blocked by excitatory amino-acid transmitters , 1990, Nature.

[35]  Carl van Vreeswijk,et al.  Patterns of Synchrony in Neural Networks with Spike Adaptation , 2001, Neural Computation.

[36]  Carson C. Chow.  Phase-locking in weakly heterogeneous neuronal networks , 1997, cond-mat/9709220.

[37]  D. Hansel,et al.  Existence and stability of persistent states in large neuronal networks. , 2001, Physical review letters.

[38]  Carson C. Chow,et al.  Synchronization and Oscillatory Dynamics in Heterogeneous, Mutually Inhibited Neurons , 1998, Journal of Computational Neuroscience.

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

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

[41]  Nancy Kopell,et al.  Synchronization in Networks of Excitatory and Inhibitory Neurons with Sparse, Random Connectivity , 2003, Neural Computation.

[42]  Xiao-Jing Wang,et al.  Alternating and Synchronous Rhythms in Reciprocally Inhibitory Model Neurons , 1992, Neural Computation.

[43]  Catherine Tallon-Baudry,et al.  Induced γ-Band Activity during the Delay of a Visual Short-Term Memory Task in Humans , 1998, The Journal of Neuroscience.

[44]  Nancy Kopell,et al.  Rapid synchronization through fast threshold modulation , 1993, Biological Cybernetics.

[45]  E. Izhikevich,et al.  Weakly connected neural networks , 1997 .

[46]  Golomb,et al.  Dynamics of globally coupled inhibitory neurons with heterogeneity. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[47]  H. Sakaguchi.  Instability of synchronized motion in nonlocally coupled neural oscillators. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[48]  R. Traub,et al.  Fast rhythmic bursting can be induced in layer 2/3 cortical neurons by enhancing persistent Na+ conductance or by blocking BK channels. , 2003, Journal of neurophysiology.

[49]  G. Ermentrout,et al.  Analysis of neural excitability and oscillations , 1989 .

[50]  J. Pernier,et al.  Induced gamma-band activity during the delay of a visual short-term memory task in humans. , 1998, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[51]  Jonathan E. Rubin,et al.  The geometry of neuronal recruitment , 2006 .

[52]  A. Destexhe,et al.  The high-conductance state of neocortical neurons in vivo , 2003, Nature Reviews Neuroscience.

[53]  A. Hodgkin.  The local electric changes associated with repetitive action in a non‐medullated axon , 1948, The Journal of physiology.

[54]  Fiona E. N. LeBeau,et al.  A model of gamma‐frequency network oscillations induced in the rat CA3 region by carbachol in vitro , 2000, The European journal of neuroscience.

[55]  N. Kopell,et al.  Dynamics of two mutually coupled slow inhibitory neurons , 1998 .

[56]  Nicolas Brunel,et al.  Fast Global Oscillations in Networks of Integrate-and-Fire Neurons with Low Firing Rates , 1999, Neural Computation.

[57]  Miles A. Whittington,et al.  New Roles for the Gamma Rhythm: Population Tuning and Preprocessing for the Beta Rhythm , 2004, Journal of Computational Neuroscience.

[58]  Eugene M. Izhikevich,et al.  Neural excitability, Spiking and bursting , 2000, Int. J. Bifurc. Chaos.

[59]  James M. Bower,et al.  Spike Frequency Adaptation Affects the Synchronization Properties of Networks of Cortical Oscillators , 1998, Neural Computation.

[60]  T J Sejnowski,et al.  Computational model of carbachol‐induced delta, theta, and gamma oscillations in the hippocampus , 2001, Hippocampus.

[61]  Nicolas Brunel,et al.  Dynamics of Sparsely Connected Networks of Excitatory and Inhibitory Spiking Neurons , 2000, Journal of Computational Neuroscience.

[62]  N. Kopell,et al.  Almost-synchronous solutions for mutually coupled excitatory neurons , 2000 .

[63]  W. Singer,et al.  Temporal coding in the visual cortex: new vistas on integration in the nervous system , 1992, Trends in Neurosciences.

[64]  Bard Ermentrout,et al.  Type I Membranes, Phase Resetting Curves, and Synchrony , 1996, Neural Computation.

[65]  R. Traub,et al.  Spatiotemporal patterns of γ frequency oscillations tetanically induced in the rat hippocampal slice , 1997 .

[66]  G. Ermentrout,et al.  Parabolic bursting in an excitable system coupled with a slow oscillation , 1986 .

[67]  P. Somogyi,et al.  Proximally targeted GABAergic synapses and gap junctions synchronize cortical interneurons , 2000, Nature Neuroscience.

[68]  K. Reinikainen,et al.  Selective attention enhances the auditory 40-Hz transient response in humans , 1993, Nature.

[69]  A. Destexhe,et al.  Impact of network activity on the integrative properties of neocortical pyramidal neurons in vivo. , 1999, Journal of neurophysiology.

[70]  R. Traub,et al.  Spatiotemporal patterns of gamma frequency oscillations tetanically induced in the rat hippocampal slice. , 1997, The Journal of physiology.

[71]  N. Birbaumer,et al.  High-frequency brain activity: Its possible role in attention, perception and language processing , 1997, Progress in Neurobiology.

[72]  R. Traub,et al.  Inhibition-based rhythms: experimental and mathematical observations on network dynamics. , 2000, International journal of psychophysiology : official journal of the International Organization of Psychophysiology.

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

[74]  Charles S. Peskin,et al.  Mathematical aspects of heart physiology , 1975 .