1,351 research outputs found
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
Entropy and information in neural spike trains: Progress on the sampling problem
The major problem in information theoretic analysis of neural responses and
other biological data is the reliable estimation of entropy--like quantities
from small samples. We apply a recently introduced Bayesian entropy estimator
to synthetic data inspired by experiments, and to real experimental spike
trains. The estimator performs admirably even very deep in the undersampled
regime, where other techniques fail. This opens new possibilities for the
information theoretic analysis of experiments, and may be of general interest
as an example of learning from limited data.Comment: 7 pages, 4 figures; referee suggested changes, accepted versio
Non-equilibrium dynamics of stochastic point processes with refractoriness
Stochastic point processes with refractoriness appear frequently in the
quantitative analysis of physical and biological systems, such as the
generation of action potentials by nerve cells, the release and reuptake of
vesicles at a synapse, and the counting of particles by detector devices. Here
we present an extension of renewal theory to describe ensembles of point
processes with time varying input. This is made possible by a representation in
terms of occupation numbers of two states: Active and refractory. The dynamics
of these occupation numbers follows a distributed delay differential equation.
In particular, our theory enables us to uncover the effect of refractoriness on
the time-dependent rate of an ensemble of encoding point processes in response
to modulation of the input. We present exact solutions that demonstrate generic
features, such as stochastic transients and oscillations in the step response
as well as resonances, phase jumps and frequency doubling in the transfer of
periodic signals. We show that a large class of renewal processes can indeed be
regarded as special cases of the model we analyze. Hence our approach
represents a widely applicable framework to define and analyze non-stationary
renewal processes.Comment: 8 pages, 4 figure
Extracting non-linear integrate-and-fire models from experimental data using dynamic I–V curves
The dynamic I–V curve method was recently introduced for the efficient experimental generation of reduced neuron models. The method extracts the response properties of a neuron while it is subject to a naturalistic stimulus that mimics in vivo-like fluctuating synaptic drive. The resulting history-dependent, transmembrane current is then projected onto a one-dimensional current–voltage relation that provides the basis for a tractable non-linear integrate-and-fire model. An attractive feature of the method is that it can be used in spike-triggered mode to quantify the distinct patterns of post-spike refractoriness seen in different classes of cortical neuron. The method is first illustrated using a conductance-based model and is then applied experimentally to generate reduced models of cortical layer-5 pyramidal cells and interneurons, in injected-current and injected- conductance protocols. The resulting low-dimensional neuron models—of the refractory exponential integrate-and-fire type—provide highly accurate predictions for spike-times. The method therefore provides a useful tool for the construction of tractable models and rapid experimental classification of cortical neurons
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