Complex evolution of spike patterns during burst propagation through feed-forward networks

Stable signal transmission is crucial for information processing by the brain. Synfire-chains, defined as feed-forward networks of spiking neurons, are a well-studied class of circuit structure that can propagate a packet of single spikes while maintaining a fixed packet profile. Here, we studied the stable propagation of spike bursts, rather than single spike activities, in a feed-forward network of a general class of excitable bursting neurons. In contrast to single spikes, bursts can propagate stably without converging to any fixed profiles. Spike timings of bursts continue to change cyclically or irregularly during propagation depending on intrinsic properties of the neurons and the coupling strength of the network. To find the conditions under which bursts lose fixed profiles, we propose an analysis based on timing shifts of burst spikes similar to the phase response analysis of limit-cycle oscillators.

[1]  T. Sejnowski,et al.  Discovering Spike Patterns in Neuronal Responses , 2004, The Journal of Neuroscience.

[2]  N. Rulkov Regularization of synchronized chaotic bursts. , 2000, Physical review letters.

[3]  John M. Beggs,et al.  Behavioral / Systems / Cognitive Neuronal Avalanches Are Diverse and Precise Activity Patterns That Are Stable for Many Hours in Cortical Slice Cultures , 2004 .

[4]  A. Sherman,et al.  Channel sharing in pancreatic beta -cells revisited: enhancement of emergent bursting by noise. , 2000, Journal of theoretical biology.

[5]  A. Reyes,et al.  Two modes of interspike interval shortening by brief transient depolarizations in cat neocortical neurons. , 1993, Journal of neurophysiology.

[6]  Ad Aertsen,et al.  Stable propagation of synchronous spiking in cortical neural networks , 1999, Nature.

[7]  F T Arecchi,et al.  Autonomous bursting in a homoclinic system. , 2001, Physical review letters.

[8]  Tomoki Fukai,et al.  Sequential associative memory with nonuniformity of the layer sizes. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Mark C. W. van Rossum,et al.  Fast Propagation of Firing Rates through Layered Networks of Noisy Neurons , 2002, The Journal of Neuroscience.

[10]  James A. Glazier,et al.  Waves in Diffusively Coupled Bursting Cells , 1999 .

[11]  John Rinzel,et al.  A Formal Classification of Bursting Mechanisms in Excitable Systems , 1987 .

[12]  Brendon O. Watson,et al.  Internal Dynamics Determine the Cortical Response to Thalamic Stimulation , 2005, Neuron.

[13]  Gregoire Nicolis,et al.  Stochastic resonance , 2007, Scholarpedia.

[14]  E. Teramoto,et al.  Mathematical Topics in Population Biology, Morphogenesis and Neurosciences , 1987 .

[15]  Jürgen Kurths,et al.  Noise-induced phase synchronization and synchronization transitions in chaotic oscillators. , 2002, Physical review letters.

[16]  J. Keizer,et al.  Minimal model for membrane oscillations in the pancreatic beta-cell. , 1983, Biophysical journal.

[17]  Martin Hasler,et al.  Synchronization of bursting neurons: what matters in the network topology. , 2005, Physical review letters.

[18]  Andrey Shilnikov,et al.  Transition between tonic spiking and bursting in a neuron model via the blue-sky catastrophe. , 2005, Physical review letters.

[19]  H. Sebastian Seung,et al.  Intrinsic bursting enhances the robustness of a neural network model of sequence generation by avian brain area HVC , 2007, Journal of Computational Neuroscience.

[20]  Y. Kuramoto,et al.  Dephasing and bursting in coupled neural oscillators. , 1995, Physical review letters.

[21]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[22]  Georgi S Medvedev,et al.  Transition to bursting via deterministic chaos. , 2006, Physical review letters.

[23]  Moshe Abeles,et al.  Corticonics: Neural Circuits of Cerebral Cortex , 1991 .

[24]  Yoshiki Kuramoto,et al.  Chemical Oscillations, Waves, and Turbulence , 1984, Springer Series in Synergetics.

[25]  Eugene M. Izhikevich,et al.  Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting , 2006 .

[26]  Tomoki Fukai,et al.  Synchronization of excitatory neurons with strongly heterogeneous phase responses. , 2007 .

[27]  A. Reyes,et al.  Layer and frequency dependencies of phase response properties of pyramidal neurons in rat motor cortex , 2007, The European journal of neuroscience.

[28]  Markus Diesmann,et al.  Activity dynamics and propagation of synchronous spiking in locally connected random networks , 2003, Biological Cybernetics.

[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]  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.

[31]  Corey D. Acker,et al.  Synchronization in hybrid neuronal networks of the hippocampal formation. , 2005, Journal of neurophysiology.

[32]  John Rinzel,et al.  Bursting phenomena in a simplified Oregonator flow system model , 1982 .

[33]  E. Vaadia,et al.  Spatiotemporal structure of cortical activity: properties and behavioral relevance. , 1998, Journal of neurophysiology.

[34]  Tomoki Fukai,et al.  Local cortical circuit model inferred from power-law distributed neuronal avalanches , 2007, Journal of Computational Neuroscience.

[35]  Tomoki Fukai,et al.  Fokker-Planck approach to the pulse packet propagation in synfire chain , 2001, Neural Networks.

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

[37]  Xiao-Jing Wang,et al.  Genesis of bursting oscillations in the Hindmarsh-Rose model and homoclinicity to a chaotic saddle , 1993 .

[38]  Tomoki Fukai,et al.  Synchronous and asynchronous bursting states: role of intrinsic neural dynamics , 2007, Journal of Computational Neuroscience.

[39]  H. Chaté,et al.  Role of defects in the transition to turbulence via spatiotemporal intermittency , 1989 .

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

[41]  David Terman,et al.  Chaotic spikes arising from a model of bursting in excitable membranes , 1991 .

[42]  Thomas Nowotny,et al.  Dynamical origin of independent spiking and bursting activity in neural microcircuits. , 2007, Physical review letters.

[43]  Jürgen Kurths,et al.  Synchronized chaotic intermittent and spiking behavior in coupled map chains. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[44]  J. C. Smith,et al.  Models of respiratory rhythm generation in the pre-Bötzinger complex. I. Bursting pacemaker neurons. , 1999, Journal of neurophysiology.

[45]  Arnéodo,et al.  Crisis-induced intermittent bursting in reaction-diffusion chemical systems. , 1992, Physical review letters.

[46]  Alain Destexhe,et al.  Neuronal Computations with Stochastic Network States , 2006, Science.

[47]  K. D. Punta,et al.  An ultra-sparse code underlies the generation of neural sequences in a songbird , 2002 .

[48]  Y. Kuramoto,et al.  Strong desynchronizing effects of weak noise in globally coupled systems. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[49]  G Bard Ermentrout,et al.  Efficient estimation of phase-resetting curves in real neurons and its significance for neural-network modeling. , 2005, Physical review letters.

[50]  Jun-nosuke Teramae,et al.  Noise Induced Phase Synchronization of a General Class of Limit Cycle Oscillators(Oscillation, Chaos and Network Dynamics in Nonlinear Science) , 2006 .

[51]  Jürgen Kurths,et al.  Phase synchronization in ensembles of bursting oscillators. , 2004, Physical review letters.