Dispersion and time delay effects in synchronized spike–burst networks

We study spike–burst neural activity and investigate its transitions to synchronized states under electrical coupling. Our reported results include the following: (1) Synchronization of spike–burst activity is a multi-time scale phenomenon and burst synchrony is easier to achieve than spike synchrony. (2) Synchrony of networks with time-delayed connections can be achieved at lower coupling strengths than within the same network with instantaneous couplings. (3) The introduction of parameter dispersion into the network destroys the existence of synchrony in the strict sense, but the network dynamics in major regimes of the parameter space can still be effectively captured by a mean field approach if the couplings are excitatory. Our results on synchronization of spiking networks are general of nature and will aid in the development of minimal models of neuronal populations. The latter are the building blocks of large scale brain networks relevant for cognitive processing.

[1]  W. Schultz,et al.  Responses of monkey dopamine neurons during learning of behavioral reactions. , 1992, Journal of neurophysiology.

[2]  W. Singer,et al.  Visuomotor integration is associated with zero time-lag synchronization among cortical areas , 1997, Nature.

[3]  R. Llinás,et al.  The functional states of the thalamus and the associated neuronal interplay. , 1988, Physiological reviews.

[4]  Kurths,et al.  Phase synchronization of chaotic oscillators. , 1996, Physical review letters.

[5]  Viktor K. Jirsa,et al.  Connectivity and dynamics of neural information processing , 2007, Neuroinformatics.

[6]  M M Mesulam,et al.  Large‐scale neurocognitive networks and distributed processing for attention, language, and memory , 1990, Annals of neurology.

[7]  Viktor K. Jirsa,et al.  Neuronal Dynamics and Brain Connectivity , 2007 .

[8]  S. Strogatz,et al.  Splay states in globally coupled Josephson arrays: Analytical prediction of Floquet multipliers. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[9]  Massimo Avoli,et al.  Generalized Epilepsy: Neurobiological Approaches , 1990 .

[10]  T. Carroll,et al.  Master Stability Functions for Synchronized Coupled Systems , 1998 .

[11]  V. Mountcastle.  Perceptual Neuroscience: The Cerebral Cortex , 1998 .

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

[13]  G Scollo-Lavizzari,et al.  [Generalized epilepsy]. , 2020, Therapeutische Umschau. Revue therapeutique.

[14]  D. Weinberger.  Implications of normal brain development for the pathogenesis of schizophrenia. , 1987, Archives of general psychiatry.

[15]  David Terman,et al.  Analysis of clustered firing patterns in synaptically coupled networks of oscillators , 2000, Journal of mathematical biology.

[16]  D. McCormick,et al.  Functional implications of burst firing and single spike activity in lateral geniculate relay neurons , 1990, Neuroscience.

[17]  G. Edelman,et al.  Reentrant signaling among simulated neuronal groups leads to coherency in their oscillatory activity. , 1989, Proceedings of the National Academy of Sciences of the United States of America.

[18]  B. Bunney,et al.  Firing properties of substantia nigra dopaminergic neurons in freely moving rats. , 1985, Life sciences.

[19]  Viktor K. Jirsa,et al.  Handbook of Brain Connectivity , 2007 .

[20]  I. Soltesz,et al.  Modulation of network behaviour by changes in variance in interneuronal properties , 2002, The Journal of physiology.

[21]  O. Bertrand,et al.  Oscillatory Synchrony between Human Extrastriate Areas during Visual Short-Term Memory Maintenance , 2001, The Journal of Neuroscience.

[22]  T. Sejnowski,et al.  Thalamocortical oscillations in the sleeping and aroused brain. , 1993, Science.

[23]  J. Hindmarsh,et al.  A model of neuronal bursting using three coupled first order differential equations , 1984, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[24]  J A Scott Kelso,et al.  Synchrony and clustering in heterogeneous networks with global coupling and parameter dispersion. , 2004, Physical review letters.

[25]  A. Treisman.  The binding problem , 1996, Current Opinion in Neurobiology.

[26]  Vivien A. Casagrande,et al.  Biophysics of Computation: Information Processing in Single Neurons , 1999 .

[27]  勇一 作村,et al.  Biophysics of Computation , 2001 .

[28]  J. Rinzel,et al.  Dissection of a model for neuronal parabolic bursting , 1987, Journal of mathematical biology.

[29]  Marcel Abendroth,et al.  Biological delay systems: Linear stability theory , 1990 .

[30]  M Steriade,et al.  Electrophysiological correlates of sleep delta waves. , 1998, Electroencephalography and clinical neurophysiology.

[31]  S. Bressler,et al.  Operational principles of neurocognitive networks. , 2006, International journal of psychophysiology : official journal of the International Organization of Psychophysiology.

[32]  C. Koch,et al.  Towards a neurobiological theory of consciousness , 1990 .

[33]  H Petsche,et al.  Synchronization between temporal and parietal cortex during multimodal object processing in man. , 1999, Cerebral cortex.

[34]  J. Kelso,et al.  Cortical coordination dynamics and cognition , 2001, Trends in Cognitive Sciences.

[35]  J. Desmedt,et al.  Transient phase-locking of 40 Hz electrical oscillations in prefrontal and parietal human cortex reflects the process of conscious somatic perception , 1994, Neuroscience Letters.

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

[37]  O. Snead,et al.  Basic mechanisms of generalized absence seizures , 1995, Annals of neurology.

[38]  J. Hindmarsh,et al.  A model of the nerve impulse using two first-order differential equations , 1982, Nature.

[39]  John G. Milton,et al.  Brain Connectivity and the Spread of Epileptic Seizures , 2007 .

[40]  S. Bressler.  The gamma wave: a cortical information carrier? , 1990, Trends in Neurosciences.

[41]  Christoph Braun,et al.  Coherence of gamma-band EEG activity as a basis for associative learning , 1999, Nature.

[42]  W. A. Wilson,et al.  The role of GABAB receptor activation in absence seizures of lethargic (lh/lh) mice. , 1992, Science.

[43]  C. Koch,et al.  The control of retinogeniculate transmission in the mammalian lateral geniculate nucleus , 2004, Experimental Brain Research.

[44]  J. Engel,et al.  Brain Reward Systems and Abuse , 1987 .

[45]  E. Bullmore,et al.  Functional Magnetic Resonance Image Analysis of a Large-Scale Neurocognitive Network , 1996, NeuroImage.

[46]  Mingzhou Ding,et al.  Enhancement of neural synchrony by time delay. , 2004, Physical review letters.

[47]  S. De Monte,et al.  Coherent regimes of globally coupled dynamical systems. , 2002, Physical review letters.

[48]  S. Strogatz,et al.  Phase diagram for the collective behavior of limit-cycle oscillators. , 1990, Physical review letters.

[49]  A. Grace,et al.  The control of firing pattern in nigral dopamine neurons: burst firing , 1984, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[50]  Buhmann.  Oscillations and low firing rates in associative memory neural networks. , 1989, Physical review. A, General physics.

[51]  M. Mesulam,et al.  From sensation to cognition. , 1998, Brain : a journal of neurology.

[52]  E. Vaadia,et al.  Spatiotemporal firing patterns in the frontal cortex of behaving monkeys. , 1993, Journal of neurophysiology.

[53]  Mingzhou Ding,et al.  Transitions to synchrony in coupled bursting neurons. , 2004, Physical review letters.

[54]  M. Umemiya,et al.  A Calcium-Dependent Feedback Mechanism Participates in Shaping Single NMDA Miniature EPSCs , 2001, The Journal of Neuroscience.

[55]  Anthony Randal McIntosh,et al.  Towards a network theory of cognition , 2000, Neural Networks.