181,887 research outputs found
On the complex dynamics of intracellular ganglion cell light responses in the cat retina
We recorded intracellular responses from cat retinal ganglion cells to sinusoidal flickering lights and compared the response dynamics to a theoretical model based on coupled nonlinear oscillators. Flicker responses for several different spot sizes were separated in a 'smooth' generator (G) potential and eorresponding spike trains. We have previously shown that the G-potential reveals complex, stimulus dependent, oscillatory behavior in response to sinusoidally flickering lights. Such behavior could be simulated by a modified van der Pol oscillator. In this paper, we extend the model to account for spike generation as well, by including extended Hodgkin-Huxley equations describing local membrane properties.
We quantified spike responses by several parameters describing the mean and standard deviation of spike burst duration, timing (phase shift) of bursts, and the number of spikes in a burst. The dependence of these response parameters on stimulus frequency and spot size could be reproduced in great detail by coupling the van der Pol oscillator, and Hodgkin-Huxley equations. The model mimics many experimentally observed response patterns, including non-phase-locked irregular oscillations. Our findings suggest that the information in the ganglion cell spike train reflects both intraretinal processing, simulated by the van der Pol oscillator) and local membrane properties described by Hodgkin-Huxley equations. The interplay between these complex processes can be simulated by changing the coupling coefficients between the two oscillators. Our simulations therefore show that irregularities in spike trains, which normally are considered to be noise, may be interpreted as complex oscillations that might earry information.Whitehall Foundation (S93-24
A simple model for low variability in neural spike trains
Neural noise sets a limit to information transmission in sensory systems. In
several areas, the spiking response (to a repeated stimulus) has shown a higher
degree of regularity than predicted by a Poisson process. However, a simple
model to explain this low variability is still lacking. Here we introduce a new
model, with a correction to Poisson statistics, which can accurately predict
the regularity of neural spike trains in response to a repeated stimulus. The
model has only two parameters, but can reproduce the observed variability in
retinal recordings in various conditions. We show analytically why this
approximation can work. In a model of the spike emitting process where a
refractory period is assumed, we derive that our simple correction can well
approximate the spike train statistics over a broad range of firing rates. Our
model can be easily plugged to stimulus processing models, like
Linear-nonlinear model or its generalizations, to replace the Poisson spike
train hypothesis that is commonly assumed. It estimates the amount of
information transmitted much more accurately than Poisson models in retinal
recordings. Thanks to its simplicity this model has the potential to explain
low variability in other areas
Linear response for spiking neuronal networks with unbounded memory
We establish a general linear response relation for spiking neuronal
networks, based on chains with unbounded memory. This relation allows us to
predict the influence of a weak amplitude time-dependent external stimuli on
spatio-temporal spike correlations, from the spontaneous statistics (without
stimulus) in a general context where the memory in spike dynamics can extend
arbitrarily far in the past. Using this approach, we show how linear response
is explicitly related to neuronal dynamics with an example, the gIF model,
introduced by M. Rudolph and A. Destexhe. This example illustrates the
collective effect of the stimuli, intrinsic neuronal dynamics, and network
connectivity on spike statistics. We illustrate our results with numerical
simulations.Comment: 60 pages, 8 figure
Sequential Desynchronization in Networks of Spiking Neurons with Partial Reset
The response of a neuron to synaptic input strongly depends on whether or not
it has just emitted a spike. We propose a neuron model that after spike
emission exhibits a partial response to residual input charges and study its
collective network dynamics analytically. We uncover a novel desynchronization
mechanism that causes a sequential desynchronization transition: In globally
coupled neurons an increase in the strength of the partial response induces a
sequence of bifurcations from states with large clusters of synchronously
firing neurons, through states with smaller clusters to completely asynchronous
spiking. We briefly discuss key consequences of this mechanism for more general
networks of biophysical neurons
Coherent response of the Hodgkin-Huxley neuron in the high-input regime
We analyze the response of the Hodgkin-Huxley neuron to a large number of
uncorrelated stochastic inhibitory and excitatory post-synaptic spike trains.
In order to clarify the various mechanisms responsible for noise-induced spike
triggering we examine the model in its silent regime. We report the coexistence
of two distinct coherence resonances: the first one at low noise is due to the
stimulation of "correlated" subthreshold oscillations; the second one at
intermediate noise variances is instead related to the regularization of the
emitted spike trains.Comment: 5 pages - 5 eps figures, contribution presented to the conference CNS
2006 held in Edinburgh (UK), to appear on Neurocomputin
Entropy-based parametric estimation of spike train statistics
We consider the evolution of a network of neurons, focusing on the asymptotic
behavior of spikes dynamics instead of membrane potential dynamics. The spike
response is not sought as a deterministic response in this context, but as a
conditional probability : "Reading out the code" consists of inferring such a
probability. This probability is computed from empirical raster plots, by using
the framework of thermodynamic formalism in ergodic theory. This gives us a
parametric statistical model where the probability has the form of a Gibbs
distribution. In this respect, this approach generalizes the seminal and
profound work of Schneidman and collaborators. A minimal presentation of the
formalism is reviewed here, while a general algorithmic estimation method is
proposed yielding fast convergent implementations. It is also made explicit how
several spike observables (entropy, rate, synchronizations, correlations) are
given in closed-form from the parametric estimation. This paradigm does not
only allow us to estimate the spike statistics, given a design choice, but also
to compare different models, thus answering comparative questions about the
neural code such as : "are correlations (or time synchrony or a given set of
spike patterns, ..) significant with respect to rate coding only ?" A numerical
validation of the method is proposed and the perspectives regarding spike-train
code analysis are also discussed.Comment: 37 pages, 8 figures, submitte
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