Dynamics of Spiking Neurons with Electrical Coupling

We analyze the existence and stability of phase-locked states of neurons coupled electrically with gap junctions. We show that spike shape and size, along with driving current (which affects network frequency), play a large role in which phase-locked modes exist and are stable. Our theory makes predictions about biophysical models using spikes of different shapes, and we present simulations to confirm the predictions. We also analyze a large system of all-to-all coupled neurons and show that the splay-phase state can exist only for a certain range of frequencies.

[1]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[2]  R. Llinás,et al.  Electrotonic coupling between neurons in cat inferior olive. , 1974, Journal of neurophysiology.

[3]  D. Spray,et al.  Physiology and pharmacology of gap junctions. , 1985, Annual review of physiology.

[4]  E. Marder,et al.  The effect of electrical coupling on the frequency of model neuronal oscillators. , 1990, Science.

[5]  J. Dowling.  Retinal neuromodulation: The role of dopamine , 1991, Visual Neuroscience.

[6]  J. Rinzel,et al.  Rhythmogenic effects of weak electrotonic coupling in neuronal models. , 1992, Proceedings of the National Academy of Sciences of the United States of America.

[7]  Wulfram Gerstner,et al.  Associative memory in a network of ‘spiking’ neurons , 1992 .

[8]  D. Spray,et al.  Gap junctions in the brain: where, what type, how many and why? , 1993, Trends in Neurosciences.

[9]  A. Sherman.  Anti-phase, asymmetric and aperiodic oscillations in excitable cells--I. Coupled bursters. , 1994, Bulletin of mathematical biology.

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

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

[12]  W. Gerstner,et al.  Time structure of the activity in neural network models. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[13]  Wulfram Gerstner,et al.  What Matters in Neuronal Locking? , 1996, Neural Computation.

[14]  J. Rinzel,et al.  Modeling N-methyl-d-aspartate-induced bursting in dopamine neurons , 1996, Neuroscience.

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

[16]  T. Sejnowski,et al.  [Letters to nature] , 1996, Nature.

[17]  Y. Kuramoto,et al.  Diffusive Interaction Leading to Dephasing of Coupled Neural Oscillators , 1997 .

[18]  M. V. Bennett,et al.  Gap junctions as electrical synapses. , 1997, Journal of neurocytology.

[19]  T. Sejnowski,et al.  Synchronous oscillatory activity in sensory systems: new vistas on mechanisms , 1997, Current Opinion in Neurobiology.

[20]  M. Bennett.  Gap junctions as electrical synapses , 1997 .

[21]  Idan Segev,et al.  Low-amplitude oscillations in the inferior olive: a model based on electrical coupling of neurons with heterogeneous channel densities. , 1997, Journal of neurophysiology.

[22]  A. Sherman,et al.  Diffusively coupled bursters: Effects of cell heterogeneity , 1998 .

[23]  L. Abbott,et al.  On the behavior of a neural oscillator electrically coupled to a bistable element , 1998 .

[24]  P. Bressloff,et al.  Desynchronization, Mode Locking, and Bursting in Strongly Coupled Integrate-and-Fire Oscillators , 1998 .

[25]  R. Traub,et al.  Electrical coupling underlies high-frequency oscillations in the hippocampus in vitro , 1998, Nature.

[26]  G B Ermentrout,et al.  Fine structure of neural spiking and synchronization in the presence of conduction delays. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[27]  N. Kopell,et al.  Dynamics of two mutually coupled slow inhibitory neurons , 1998 .

[28]  Carson C. Chow.  Phase-locking in weakly heterogeneous neuronal networks , 1997, cond-mat/9709220.

[29]  F. Skinner,et al.  Slow Oscillations (≤1 Hz) Mediated by GABAergic Interneuronal Networks in Rat Hippocampus , 1998, The Journal of Neuroscience.

[30]  J. Velazquez,et al.  Bursting in inhibitory interneuronal networks: A role for gap-junctional coupling. , 1999, Journal of neurophysiology.

[31]  B. Connors,et al.  Two networks of electrically coupled inhibitory neurons in neocortex , 1999, Nature.

[32]  R. Traub,et al.  High-frequency population oscillations are predicted to occur in hippocampal pyramidal neuronal networks interconnected by axoaxonal gap junctions , 1999, Neuroscience.

[33]  Stephen Coombes,et al.  Dynamics of Strongly Coupled Spiking Neurons , 2000, Neural Computation.

[34]  T. Sejnowski,et al.  Precision of the pacemaker nucleus in a weakly electric fish: network versus cellular influences. , 2000, Journal of neurophysiology.

[35]  T. Sejnowski,et al.  Gap junction effects on precision and frequency of a model pacemaker network. , 2000, Journal of neurophysiology.

[36]  T J Lewis,et al.  Self-organized synchronous oscillations in a network of excitable cells coupled by gap junctions , 2000, Network.

[37]  N. Kopell,et al.  Almost-synchronous solutions for mutually coupled excitatory neurons , 2000 .

[38]  J. Velazquez,et al.  Artificial electrotonic coupling affects neuronal firing patterns depending upon cellular characteristics , 2001, Neuroscience.