Diverse population-bursting modes of adapting spiking neurons.

We study the dynamics of a noisy network of spiking neurons with spike-frequency adaptation (SFA), using a mean-field approach, in terms of a two-dimensional Fokker-Planck equation for the membrane potential of the neurons and the calcium concentration gating SFA. The long time scales of SFA allow us to use an adiabatic approximation and to describe the network as an effective nonlinear two-dimensional system. The phase diagram is computed for varying levels of SFA and synaptic coupling. Two different population-bursting regimes emerge, depending on the level of SFA in networks with noisy emission rate, due to the finite number of neurons.

[1]  Carl van Vreeswijk,et al.  Patterns of Synchrony in Neural Networks with Spike Adaptation , 2001, Neural Computation.

[2]  Maurizio Mattia,et al.  Frequency-dependent response properties of adapting spiking neurons. , 2007, Mathematical biosciences.

[3]  Andreas V. M. Herz,et al.  A Universal Model for Spike-Frequency Adaptation , 2003, Neural Computation.

[4]  Shimon Marom,et al.  Development, learning and memory in large random networks of cortical neurons: lessons beyond anatomy , 2002, Quarterly Reviews of Biophysics.

[5]  Henry Markram,et al.  Spike frequency adaptation and neocortical rhythms. , 2002, Journal of neurophysiology.

[6]  M. Stocker.  Ca2+-activated K+ channels: molecular determinants and function of the SK family , 2004, Nature Reviews Neuroscience.

[7]  Y. Amitai,et al.  Propagating neuronal discharges in neocortical slices: computational and experimental study. , 1997, Journal of neurophysiology.

[8]  J. Cowan,et al.  Excitatory and inhibitory interactions in localized populations of model neurons. , 1972, Biophysical journal.

[9]  N. Lesica,et al.  Encoding of Natural Scene Movies by Tonic and Burst Spikes in the Lateral Geniculate Nucleus , 2004, The Journal of Neuroscience.

[10]  M Giugliano,et al.  Single-neuron discharge properties and network activity in dissociated cultures of neocortex. , 2004, Journal of neurophysiology.

[11]  B. Richmond,et al.  Intrinsic dynamics in neuronal networks. I. Theory. , 2000, Journal of neurophysiology.

[12]  Maurizio Mattia,et al.  Finite-size dynamics of inhibitory and excitatory interacting spiking neurons. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Eisaku Maeda,et al.  Experimental analysis of neuronal dynamics in cultured cortical networks and transitions between different patterns of activity , 1997, Biological Cybernetics.

[14]  勇一 作村,et al.  Biophysics of Computation , 2001 .

[15]  Y Shapira,et al.  Observations and modeling of synchronized bursting in two-dimensional neural networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  B. Richmond,et al.  Intrinsic dynamics in neuronal networks. II. experiment. , 2000, Journal of neurophysiology.

[17]  Maurizio Mattia,et al.  Collective Behavior of Networks with Linear (VLSI) Integrate-and-Fire Neurons , 1999, Neural Computation.

[18]  Li I. Zhang,et al.  Electrical activity and development of neural circuits , 2001, Nature Neuroscience.

[19]  C. Koch,et al.  From stimulus encoding to feature extraction in weakly electric fish , 1996, Nature.

[20]  M. Corner,et al.  Physiological effects of sustained blockade of excitatory synaptic transmission on spontaneously active developing neuronal networks—an inquiry into the reciprocal linkage between intrinsic biorhythms and neuroplasticity in early ontogeny , 2002, Neuroscience & Biobehavioral Reviews.

[21]  Y. Ben-Ari.  Developing networks play a similar melody , 2001, Trends in Neurosciences.

[22]  X J Wang,et al.  Calcium coding and adaptive temporal computation in cortical pyramidal neurons. , 1998, Journal of neurophysiology.

[23]  J. Lisman.  Bursts as a unit of neural information: making unreliable synapses reliable , 1997, Trends in Neurosciences.

[24]  M. Mattia,et al.  Population dynamics of interacting spiking neurons. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  R. FitzHugh.  Impulses and Physiological States in Theoretical Models of Nerve Membrane. , 1961, Biophysical journal.

[26]  Brent Doiron,et al.  Parallel Processing of Sensory Input by Bursts and Isolated Spikes , 2004, The Journal of Neuroscience.