Interplay between excitability type and distributions of neuronal connectivity determines neuronal network synchronization.

While the interplay between neuronal excitability properties and global properties of network topology is known to affect network propensity for synchronization, it is not clear how detailed characteristics of these properties affect spatiotemporal pattern formation. Here we study mixed networks, composed of neurons having type I and/or type II phase response curves, with varying distributions of local and random connections and show that not only average network properties, but also the connectivity distribution statistics, significantly affect network synchrony. Namely, we study networks with fixed networkwide properties, but vary the number of random connections that nodes project. We show that varying node excitability (type I vs type II) influences network synchrony most dramatically for systems with long-tailed distributions of the number of random connections per node. This indicates that a cluster of even a few highly rewired cells with a high propensity for synchronization can alter the degree of synchrony in the network as a whole. We show this effect generally on a network of coupled Kuramoto oscillators and investigate the impact of this effect more thoroughly in pulse-coupled networks of biophysical neurons.

[1]  V. Booth,et al.  Synchronization properties of heterogeneous neuronal networks with mixed excitability type. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  S. Boccaletti,et al.  Complex network theory and the brain , 2014, Philosophical Transactions of the Royal Society B: Biological Sciences.

[3]  M. P. van den Heuvel,et al.  Rich Club Organization and Intermodule Communication in the Cat Connectome , 2013, The Journal of Neuroscience.

[4]  Cedric E. Ginestet,et al.  Cognitive relevance of the community structure of the human brain functional coactivation network , 2013, Proceedings of the National Academy of Sciences.

[5]  Emma K. Towlson,et al.  The Rich Club of the C. elegans Neuronal Connectome , 2013, The Journal of Neuroscience.

[6]  Kaspar Anton Schindler,et al.  Synchronization and desynchronization in epilepsy: controversies and hypotheses , 2012, The Journal of physiology.

[7]  O. Sporns,et al.  High-cost, high-capacity backbone for global brain communication , 2012, Proceedings of the National Academy of Sciences.

[8]  O. Sporns,et al.  Rich-Club Organization of the Human Connectome , 2011, The Journal of Neuroscience.

[9]  Vito Latora,et al.  Emergence of structural patterns out of synchronization in networks with competitive interactions , 2011, Scientific reports.

[10]  M. Delong,et al.  Milestones in research on the pathophysiology of Parkinson's disease , 2011, Movement disorders : official journal of the Movement Disorder Society.

[11]  Victoria Booth,et al.  Cellularly-Driven Differences in Network Synchronization Propensity Are Differentially Modulated by Firing Frequency , 2011, PLoS Comput. Biol..

[12]  U. Rutishauser,et al.  Human memory strength is predicted by theta-frequency phase-locking of single neurons , 2010, Nature.

[13]  W. Singer,et al.  Abnormal neural oscillations and synchrony in schizophrenia , 2010, Nature Reviews Neuroscience.

[14]  Michel A. Picardo,et al.  GABAergic Hub Neurons Orchestrate Synchrony in Developing Hippocampal Networks , 2009, Science.

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

[16]  Boris S. Gutkin,et al.  The effects of cholinergic neuromodulation on neuronal phase-response curves of modeled cortical neurons , 2009, Journal of Computational Neuroscience.

[17]  Han Fang,et al.  Complete and phase synchronization in a heterogeneous small-world neuronal network , 2009 .

[18]  Victoria Booth,et al.  Interaction of Cellular and Network Mechanisms in Spatiotemporal Pattern Formation in Neuronal Networks , 2009, The Journal of Neuroscience.

[19]  T. Sejnowski,et al.  Cholinergic Neuromodulation Changes Phase Response Curve Shape and Type in Cortical Pyramidal Neurons , 2008, PloS one.

[20]  Jurgen Kurths,et al.  Synchronization in complex networks , 2008, 0805.2976.

[21]  G Bard Ermentrout,et al.  Class-II neurons display a higher degree of stochastic synchronization than class-I neurons. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  R. Morgan,et al.  Nonrandom connectivity of the epileptic dentate gyrus predicts a major role for neuronal hubs in seizures , 2008, Proceedings of the National Academy of Sciences.

[23]  Shan Yu,et al.  A Small World of Neuronal Synchrony , 2008, Cerebral cortex.

[24]  L. Tsimring,et al.  Topological determinants of epileptogenesis in large-scale structural and functional models of the dentate gyrus derived from experimental data. , 2007, Journal of neurophysiology.

[25]  W. Singer,et al.  Neural Synchrony in Brain Disorders: Relevance for Cognitive Dysfunctions and Pathophysiology , 2006, Neuron.

[26]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[27]  G. Ermentrout,et al.  Phase-response curves give the responses of neurons to transient inputs. , 2005, Journal of neurophysiology.

[28]  E. Vaadia,et al.  Spike Synchronization in the Cortex-Basal Ganglia Networks of Parkinsonian Primates Reflects Global Dynamics of the Local Field Potentials , 2004, The Journal of Neuroscience.

[29]  John M. Beggs,et al.  Neuronal Avalanches in Neocortical Circuits , 2003, The Journal of Neuroscience.

[30]  Chunguang Li,et al.  Stability of a neural network model with small-world connections. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  C. Elger,et al.  Human memory formation is accompanied by rhinal–hippocampal coupling and decoupling , 2001, Nature Neuroscience.

[32]  R. Desimone,et al.  Modulation of Oscillatory Neuronal Synchronization by Selective Visual Attention , 2001, Science.

[33]  S. Strogatz.  From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators , 2000 .

[34]  E. Niebur,et al.  Growth patterns in the developing brain detected by using continuum mechanical tensor maps , 2022 .

[35]  A. Jongen-Rêlo,et al.  Highly Specific Neuron Loss Preserves Lateral Inhibitory Circuits in the Dentate Gyrus of Kainate-Induced Epileptic Rats , 1999, The Journal of Neuroscience.

[36]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

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

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

[39]  Ivan Soltesz,et al.  Role of mossy fiber sprouting and mossy cell loss in hyperexcitability: a network model of the dentate gyrus incorporating cell types and axonal topography. , 2005, Journal of neurophysiology.

[40]  A. Barabasi,et al.  Emergence of Scaling in Random Networks , 1999 .