Comparision between spike and rate models in networks
of integrate-and-fire neurons
F. Chapeau-Blondeau
in Biophysical Neural Networks: Foundations of Integrative
Neuroscience
Chap. 11, R. R. Poznanski, ed., Mary Ann Liebert Inc.
(New York) 2001.
Abstract.
A neural network model is developed, based on a description of neuron
membrane conductances to govern the dynamics of action potentials. The
variables are endowed with realistic physical units and plausible numerical
values in order to reach both qualitative and quantitative significance.
At the same time, the model is kept simple enough to enable its application
to the study of collective behaviors among large populations of interacting
neurons. This model is used here to investigate the relations between spike
and rate representations of neural activities. First, the conditions for
the derivation of a neuron transfer function when the spikes are replaced
by firing rates are examined, and it is shown that such a transfer function
on rates is usually not invariant for a given neuron, but it may vary with
the statistics of the inputs. Next, a complete reduction of the network
model operating with spikes to a model operating with firing rates is carried
out. The spike and the rate models are then explicitly compared for the
description of various neural phenomena. These phenomena include self-sustained
network dynamics, the locking of a neural chain into an oscillatory activity,
and noise-enhancement of neural signal transmission via stochastic resonance.
In all cases, the comparison is done in stationary states of the networks,
and it examines neuron firing rates either as they are directly produced
by the rate model or as they are computed by explicit time averaging on
spike trains in the spike model. Dissimilarities between the descriptions
based on spikes or rates are especially pointed out. The present study
contributes to a better appreciation of the possibilities of spike and
firing rate models, and more generally, of different modeling strategies
existing for neural networks.
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