Modulation of excitatory synaptic coupling facilitates synchronization and complex dynamics in a biophysical model of neuronal dynamics

In this paper, complex dynamical synchronization in a non-linear model of a neural system is studied, and the computational significance of the behaviours is explored. The local neural dynamics is determined by voltage-and ligand-gated ion channels and feedback between densely interconnected excitatory and inhibitory neurons. A mesoscopic array of local networks is modelled by introducing coupling between the local networks via weak excitatory-to-excitatory connectivity. It is shown that with modulation of this long-range synaptic coupling, the system undergoes a transition from independent oscillations to stable chaotic synchronization. Between these states exists a ‘weakly’ stable state associated with complex, intermittent behaviour in the temporal domain and clusters of synchronous regions in the spatial domain. The paper concludes with a discussion of the putative relevance of such processes in the brain, including the role of neuromodulatory systems and the mechanisms underlying sensory perception, adaptation, computation and complexity.

[1]  Lila L. Gatlin,et al.  Information theory and the living system , 1972 .

[2]  C. Morris,et al.  Voltage oscillations in the barnacle giant muscle fiber. , 1981, Biophysical journal.

[3]  H. Fujisaka,et al.  Stability Theory of Synchronized Motion in Coupled-Oscillator Systems , 1983 .

[4]  J. Szentágothai.  The modular architectonic principle of neural centers. , 1983, Reviews of physiology, biochemistry and pharmacology.

[5]  M. Rabinovich,et al.  Stochastic synchronization of oscillation in dissipative systems , 1986 .

[6]  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.

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

[8]  Richard S. Sutton,et al.  Time-Derivative Models of Pavlovian Reinforcement , 1990 .

[9]  Xin Wang,et al.  Period-doublings to chaos in a simple neural network , 1991, IJCNN-91-Seattle International Joint Conference on Neural Networks.

[10]  P König,et al.  Synchronization of oscillatory neuronal responses between striate and extrastriate visual cortical areas of the cat. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[11]  P. Grassberger,et al.  Symmetry breaking bifurcation for coupled chaotic attractors , 1991 .

[12]  Hansel,et al.  Synchronization and computation in a chaotic neural network. , 1992, Physical review letters.

[13]  G. Edelman.  Neural Darwinism: Selection and reentrant signaling in higher brain function , 1993, Neuron.

[14]  G. Edelman,et al.  A measure for brain complexity: relating functional segregation and integration in the nervous system. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[15]  E. Ott,et al.  Blowout bifurcations: the occurrence of riddled basins and on-off intermittency , 1994 .

[16]  Deliang Wang,et al.  Global competition and local cooperation in a network of neural oscillators , 1995 .

[17]  Carroll,et al.  Desynchronization by periodic orbits. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[18]  Karl J. Friston,et al.  Characterising the complexity of neuronal interactions , 1995 .

[19]  L. Tsimring,et al.  Generalized synchronization of chaos in directionally coupled chaotic systems. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[20]  Nancy Kopell,et al.  Waves and synchrony in networks of oscillators of relaxation and non-relaxation type , 1995 .

[21]  Frank Pasemann,et al.  SYNCHRONOUS CHAOS IN HIGH-DIMENSIONAL MODULAR NEURAL NETWORKS , 1996 .

[22]  Yoshisuke Ueda,et al.  Riddled basins of the optimal states in learning dynamical systems , 1996 .

[23]  H. Abarbanel,et al.  Generalized synchronization of chaos: The auxiliary system approach. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[24]  R. Burke,et al.  Detecting dynamical interdependence and generalized synchrony through mutual prediction in a neural ensemble. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[26]  J. Kurths,et al.  From Phase to Lag Synchronization in Coupled Chaotic Oscillators , 1997 .

[27]  G. Edelman,et al.  Neural dynamics in a model of the thalamocortical system. II. The role of neural synchrony tested through perturbations of spike timing. , 1997, Cerebral cortex.

[28]  N. Rulkov,et al.  Robustness of Synchronized Chaotic Oscillations , 1997 .

[29]  Grigory V. Osipov,et al.  PHASE SYNCHRONIZATION EFFECTS IN A LATTICE OF NONIDENTICAL ROSSLER OSCILLATORS , 1997 .

[30]  Kunihiko Kaneko,et al.  On the strength of attractors in a high-dimensional system: Milnor attractor network, robust global attraction, and noise-induced selection , 1998, chao-dyn/9802016.

[31]  Krešimir Josić,et al.  INVARIANT MANIFOLDS AND SYNCHRONIZATION OF COUPLED DYNAMICAL SYSTEMS , 1998 .

[32]  Jürgen Kurths,et al.  Detection of n:m Phase Locking from Noisy Data: Application to Magnetoencephalography , 1998 .

[33]  E. Mosekilde,et al.  TRANSVERSE INSTABILITY AND RIDDLED BASINS IN A SYSTEM OF TWO COUPLED LOGISTIC MAPS , 1998 .

[34]  Jürgen Kurths,et al.  Alternating Locking Ratios in Imperfect Phase Synchronization , 1999 .

[35]  R. Larter,et al.  A coupled ordinary differential equation lattice model for the simulation of epileptic seizures. , 1999, Chaos.

[36]  Rajesh P. N. Rao,et al.  Predictive coding in the visual cortex: a functional interpretation of some extra-classical receptive-field effects. , 1999 .

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

[38]  Karl J. Friston.  The labile brain. II. Transients, complexity and selection. , 2000, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[39]  Karl J. Friston.  The labile brain. I. Neuronal transients and nonlinear coupling. , 2000, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[40]  U Parlitz,et al.  Robust synchronization of chaotic systems. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[41]  Liang Zhao,et al.  A network of dynamically coupled chaotic maps for scene segmentation , 2001, IEEE Trans. Neural Networks.

[42]  T. Sejnowski,et al.  Fluctuating synaptic conductances recreate in vivo-like activity in neocortical neurons , 2001, Neuroscience.

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

[44]  Michael Breakspear,et al.  Perception of Odors by a Nonlinear Model of the Olfactory Bulb , 2001, Int. J. Neural Syst..

[45]  Peter A. Tass,et al.  Desynchronization of brain rhythms with soft phase-resetting techniques , 2002, Biological Cybernetics.

[46]  John R. Terry,et al.  NONLINEAR INTERDEPENDENCE IN NEURAL SYSTEMS: MOTIVATION, THEORY, AND RELEVANCE , 2002, The International journal of neuroscience.

[47]  John R. Terry,et al.  Detection and description of non-linear interdependence in normal multichannel human EEG data , 2002, Clinical Neurophysiology.

[48]  M. Breakspear.  Nonlinear phase desynchronization in human electroencephalographic data , 2002, Human brain mapping.

[49]  Michael Breakspear,et al.  An improved algorithm for the detection of dynamical interdependence in bivariate time-series , 2003, Biological Cybernetics.

[50]  R. Eckhorn,et al.  Coherent oscillations: A mechanism of feature linking in the visual cortex? , 1988, Biological Cybernetics.

[51]  Haim Sompolinsky,et al.  Chaos and synchrony in a model of a hypercolumn in visual cortex , 1996, Journal of Computational Neuroscience.