Zero-Lag Synchronization Despite Inhomogeneities in a Relay System

A novel proposal for the zero-lag synchronization of the delayed coupled neurons, is to connect them indirectly via a third relay neuron. In this study, we develop a Poincaré map to investigate the robustness of the synchrony in such a relay system against inhomogeneity in the neurons and synaptic parameters. We show that when the inhomogeneity does not violate the symmetry of the system, synchrony is maintained and in some cases inhomogeneity enhances synchrony. On the other hand if the inhomogeneity breaks the symmetry of the system, zero lag synchrony can not be preserved. In this case we give analytical results for the phase lag of the spiking of the neurons in the stable state.

[1]  A Valizadeh,et al.  Effect of synaptic plasticity on the structure and dynamics of disordered networks of coupled neurons. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Eric Shea-Brown,et al.  On the Phase Reduction and Response Dynamics of Neural Oscillator Populations , 2004, Neural Computation.

[3]  A. Aertsen,et al.  Spike synchronization and rate modulation differentially involved in motor cortical function. , 1997, Science.

[4]  Carmen C. Canavier,et al.  Effects of conduction delays on the existence and stability of one to one phase locking between two pulse-coupled oscillators , 2011, Journal of Computational Neuroscience.

[5]  B. H. Bland,et al.  Theta band oscillation and synchrony in the hippocampal formation and associated structures: the case for its role in sensorimotor integration , 2001, Behavioural Brain Research.

[6]  R. Eckhorn,et al.  Stimulus-specific fast oscillations at zero phase between visual areas V1 and V2 of awake monkey. , 1994, Neuroreport.

[7]  Ingo Bojak,et al.  When Long-Range Zero-Lag Synchronization is Feasible in Cortical Networks , 2012, Front. Comput. Neurosci..

[8]  J. T. Murphy,et al.  Cross Correlation Studies in Primate Motor Cortex: Synaptic Interaction and Shared Input , 1985, Canadian Journal of Neurological Sciences / Journal Canadien des Sciences Neurologiques.

[9]  S. Strogatz,et al.  Time Delay in the Kuramoto Model of Coupled Oscillators , 1998, chao-dyn/9807030.

[10]  T. Womelsdorf,et al.  The role of neuronal synchronization in selective attention , 2007, Current Opinion in Neurobiology.

[11]  T. Geisel,et al.  Delay-induced multistable synchronization of biological oscillators , 1998 .

[12]  A. Pérez-Villalba.  Rhythms of the Brain, G. Buzsáki. Oxford University Press, Madison Avenue, New York (2006), Price: GB £42.00, p. 448, ISBN: 0-19-530106-4 , 2008 .

[13]  F. Varela,et al.  Perception's shadow: long-distance synchronization of human brain activity , 1999, Nature.

[14]  T. Sejnowski,et al.  Control of Spatiotemporal Coherence of a Thalamic Oscillation by Corticothalamic Feedback , 1996, Science.

[15]  S. K. Dana,et al.  Enhancing synchrony in chaotic oscillators by dynamic relaying. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  D. Hansel,et al.  On the Distribution of Firing Rates in Networks of Cortical Neurons , 2011, The Journal of Neuroscience.

[17]  Ad Aertsen,et al.  Coding and Computation in the Cortex: Single-Neuron Activity and Cooperative Phenomena , 1992 .

[18]  S. Strogatz,et al.  Phase diagram for the Winfree model of coupled nonlinear oscillators. , 2000, Physical review letters.

[19]  Leonardo L. Gollo,et al.  Dynamical relaying can yield zero time lag neuronal synchrony despite long conduction delays , 2008, Proceedings of the National Academy of Sciences.

[20]  H. Markram,et al.  t Synchrony Generation in Recurrent Networks with Frequency-Dependent Synapses , 2000, The Journal of Neuroscience.

[21]  C. Canavier,et al.  Phase-Resetting Curves Determine Synchronization, Phase Locking, and Clustering in Networks of Neural Oscillators , 2009, The Journal of Neuroscience.

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

[23]  Leonardo L. Gollo,et al.  Theta Band Zero-Lag Long-Range Cortical Synchronization via Hippocampal Dynamical Relaying , 2011, PloS one.

[24]  Carmen C. Canavier,et al.  Phase response curve , 2006, Scholarpedia.

[25]  R. Traub,et al.  A mechanism for generation of long-range synchronous fast oscillations in the cortex , 1996, Nature.

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

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

[28]  T. Sejnowski,et al.  Model of Transient Oscillatory Synchronization in the Locust Antennal Lobe , 2001, Neuron.

[29]  J. Teramae,et al.  Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators. , 2004, Physical review letters.

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

[31]  Jan Danckaert,et al.  Synchronization and symmetry breaking of delay-coupled oscillators: on the role of phase and amplitude instabilities , 2010, Photonics Europe.

[32]  Eugene M. Izhikevich,et al.  Polychronization: Computation with Spikes , 2006, Neural Computation.

[33]  O. Sporns,et al.  Motifs in Brain Networks , 2004, PLoS biology.

[34]  G. Ermentrout,et al.  Synchrony, stability, and firing patterns in pulse-coupled oscillators , 2002 .

[35]  Ernst,et al.  Synchronization induced by temporal delays in pulse-coupled oscillators. , 1995, Physical review letters.

[36]  Boris S. Gutkin,et al.  The Effects of Spike Frequency Adaptation and Negative Feedback on the Synchronization of Neural Oscillators , 2001, Neural Computation.

[37]  E. Fetz,et al.  Coherent 25- to 35-Hz oscillations in the sensorimotor cortex of awake behaving monkeys. , 1992, Proceedings of the National Academy of Sciences of the United States of America.

[38]  S. Sadeghi,et al.  Synchronization of delayed coupled neurons in presence of inhomogeneity , 2012, Journal of Computational Neuroscience.

[39]  P. Dayan.  Fast oscillations in cortical circuits , 2000 .

[40]  George L. Gerstein,et al.  Feature-linked synchronization of thalamic relay cell firing induced by feedback from the visual cortex , 1994, Nature.

[41]  S Yanchuk,et al.  Synchronizing distant nodes: a universal classification of networks. , 2010, Physical review letters.

[42]  W. Singer,et al.  Synchronization of Visual Responses between the Cortex, Lateral Geniculate Nucleus, and Retina in the Anesthetized Cat , 1998, The Journal of Neuroscience.

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

[44]  Ingo Fischer,et al.  Synchronization properties of three delay-coupled semiconductor lasers. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[45]  Olaf Sporns,et al.  Network structure of cerebral cortex shapes functional connectivity on multiple time scales , 2007, Proceedings of the National Academy of Sciences.

[46]  Leon Glass,et al.  The Shape of Phase-Resetting Curves in Oscillators with a Saddle Node on an Invariant Circle Bifurcation , 2012, Neural Computation.

[47]  W. Singer,et al.  Stimulus‐Dependent Neuronal Oscillations in Cat Visual Cortex: Receptive Field Properties and Feature Dependence , 1990, The European journal of neuroscience.

[48]  G Bard Ermentrout,et al.  Phase-response curves and synchronized neural networks , 2010, Philosophical Transactions of the Royal Society B: Biological Sciences.

[49]  D. Contreras,et al.  Spike-wave complexes and fast components of cortically generated seizures. I. Role of neocortex and thalamus. , 1998, Journal of neurophysiology.

[50]  Tianping Chen,et al.  Synchronization of coupled connected neural networks with delays , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[51]  Thomas Nowotny,et al.  Enhancement of Synchronization in a Hybrid Neural Circuit by Spike-Timing Dependent Plasticity , 2003, The Journal of Neuroscience.

[52]  P. Fries.  A mechanism for cognitive dynamics: neuronal communication through neuronal coherence , 2005, Trends in Cognitive Sciences.

[53]  G. Bard Ermentrout,et al.  Phase Response Curves to Measure Ion Channel Effects on Neurons , 2012 .

[54]  W. Singer,et al.  Modulation of Neuronal Interactions Through Neuronal Synchronization , 2007, Science.

[55]  Philipp Hövel,et al.  Synchronization of Coupled Neural oscillators with Heterogeneous delays , 2012, Int. J. Bifurc. Chaos.

[56]  Raul Vicente,et al.  Zero-lag long-range synchronization via dynamical relaying. , 2006, Physical review letters.

[57]  S. Boccaletti,et al.  Synchronization is enhanced in weighted complex networks. , 2005, Physical review letters.

[58]  J. Nadal,et al.  What can we learn from synaptic weight distributions? , 2007, Trends in Neurosciences.

[59]  W. Singer,et al.  Stimulus-specific neuronal oscillations in orientation columns of cat visual cortex. , 1989, Proceedings of the National Academy of Sciences of the United States of America.

[60]  David Hansel,et al.  The Role of Intrinsic Cell Properties in Synchrony of Neurons Interacting via Electrical Synapses , 2012 .

[61]  Leonardo L. Gollo,et al.  Dynamic control for synchronization of separated cortical areas through thalamic relay , 2010, NeuroImage.

[62]  G. Laurent,et al.  Multiplexing using synchrony in the zebrafish olfactory bulb , 2004, Nature Neuroscience.

[63]  David Terman,et al.  Mathematical foundations of neuroscience , 2010 .

[64]  Jan Karbowski,et al.  Synchrony arising from a balanced synaptic plasticity in a network of heterogeneous neural oscillators. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[65]  Kimron Shapiro,et al.  Modulation of long-range neural synchrony reflects temporal limitations of visual attention in humans. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

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

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

[68]  P. Fries.  Neuronal gamma-band synchronization as a fundamental process in cortical computation. , 2009, Annual review of neuroscience.

[69]  Neil McNaughton,et al.  Coupling of theta oscillations between anterior and posterior midline cortex and with the hippocampus in freely behaving rats. , 2009, Cerebral cortex.

[70]  G. Buzsáki,et al.  Neuronal Oscillations in Cortical Networks , 2004, Science.

[71]  W. Ditto,et al.  Taming spatiotemporal chaos with disorder , 1995, Nature.

[72]  Olaf Sporns,et al.  Mechanisms of Zero-Lag Synchronization in Cortical Motifs , 2013, PLoS Comput. Biol..

[73]  I Kanter,et al.  Zero lag synchronization of chaotic systems with time delayed couplings. , 2010, Physical review letters.

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

[75]  Alireza Valizadeh,et al.  Single phase-slip junction site can synchronize a parallel superconducting array of linearly coupled Josephson junctions , 2010 .