4,738 research outputs found
A comparative study of different integrate-and-fire neurons: spontaneous activity, dynamical response, and stimulus-induced correlation
Stochastic integrate-and-fire (IF) neuron models have found widespread
applications in computational neuroscience. Here we present results on the
white-noise-driven perfect, leaky, and quadratic IF models, focusing on the
spectral statistics (power spectra, cross spectra, and coherence functions) in
different dynamical regimes (noise-induced and tonic firing regimes with low or
moderate noise). We make the models comparable by tuning parameters such that
the mean value and the coefficient of variation of the interspike interval
match for all of them. We find that, under these conditions, the power spectrum
under white-noise stimulation is often very similar while the response
characteristics, described by the cross spectrum between a fraction of the
input noise and the output spike train, can differ drastically. We also
investigate how the spike trains of two neurons of the same kind (e.g. two
leaky IF neurons) correlate if they share a common noise input. We show that,
depending on the dynamical regime, either two quadratic IF models or two leaky
IFs are more strongly correlated. Our results suggest that, when choosing among
simple IF models for network simulations, the details of the model have a
strong effect on correlation and regularity of the output.Comment: 12 page
Timescales of spike-train correlation for neural oscillators with common drive
We examine the effect of the phase-resetting curve (PRC) on the transfer of
correlated input signals into correlated output spikes in a class of neural
models receiving noisy, super-threshold stimulation. We use linear response
theory to approximate the spike correlation coefficient in terms of moments of
the associated exit time problem, and contrast the results for Type I vs. Type
II models and across the different timescales over which spike correlations can
be assessed. We find that, on long timescales, Type I oscillators transfer
correlations much more efficiently than Type II oscillators. On short
timescales this trend reverses, with the relative efficiency switching at a
timescale that depends on the mean and standard deviation of input currents.
This switch occurs over timescales that could be exploited by downstream
circuits
Are the input parameters of white-noise-driven integrate-and-fire neurons uniquely determined by rate and CV?
Integrate-and-fire (IF) neurons have found widespread applications in
computational neuroscience. Particularly important are stochastic versions of
these models where the driving consists of a synaptic input modeled as white
Gaussian noise with mean and noise intensity . Different IF models
have been proposed, the firing statistics of which depends nontrivially on the
input parameters and . In order to compare these models among each
other, one must first specify the correspondence between their parameters. This
can be done by determining which set of parameters (, ) of each model
is associated to a given set of basic firing statistics as, for instance, the
firing rate and the coefficient of variation (CV) of the interspike interval
(ISI). However, it is not clear {\em a priori} whether for a given firing rate
and CV there is only one unique choice of input parameters for each model. Here
we review the dependence of rate and CV on input parameters for the perfect,
leaky, and quadratic IF neuron models and show analytically that indeed in
these three models the firing rate and the CV uniquely determine the input
parameters
Locking of correlated neural activity to ongoing oscillations
Population-wide oscillations are ubiquitously observed in mesoscopic signals
of cortical activity. In these network states a global oscillatory cycle
modulates the propensity of neurons to fire. Synchronous activation of neurons
has been hypothesized to be a separate channel of signal processing information
in the brain. A salient question is therefore if and how oscillations interact
with spike synchrony and in how far these channels can be considered separate.
Experiments indeed showed that correlated spiking co-modulates with the static
firing rate and is also tightly locked to the phase of beta-oscillations. While
the dependence of correlations on the mean rate is well understood in
feed-forward networks, it remains unclear why and by which mechanisms
correlations tightly lock to an oscillatory cycle. We here demonstrate that
such correlated activation of pairs of neurons is qualitatively explained by
periodically-driven random networks. We identify the mechanisms by which
covariances depend on a driving periodic stimulus. Mean-field theory combined
with linear response theory yields closed-form expressions for the
cyclostationary mean activities and pairwise zero-time-lag covariances of
binary recurrent random networks. Two distinct mechanisms cause time-dependent
covariances: the modulation of the susceptibility of single neurons (via the
external input and network feedback) and the time-varying variances of single
unit activities. For some parameters, the effectively inhibitory recurrent
feedback leads to resonant covariances even if mean activities show
non-resonant behavior. Our analytical results open the question of
time-modulated synchronous activity to a quantitative analysis.Comment: 57 pages, 12 figures, published versio
A unified view on weakly correlated recurrent networks
The diversity of neuron models used in contemporary theoretical neuroscience
to investigate specific properties of covariances raises the question how these
models relate to each other. In particular it is hard to distinguish between
generic properties and peculiarities due to the abstracted model. Here we
present a unified view on pairwise covariances in recurrent networks in the
irregular regime. We consider the binary neuron model, the leaky
integrate-and-fire model, and the Hawkes process. We show that linear
approximation maps each of these models to either of two classes of linear rate
models, including the Ornstein-Uhlenbeck process as a special case. The classes
differ in the location of additive noise in the rate dynamics, which is on the
output side for spiking models and on the input side for the binary model. Both
classes allow closed form solutions for the covariance. For output noise it
separates into an echo term and a term due to correlated input. The unified
framework enables us to transfer results between models. For example, we
generalize the binary model and the Hawkes process to the presence of
conduction delays and simplify derivations for established results. Our
approach is applicable to general network structures and suitable for
population averages. The derived averages are exact for fixed out-degree
network architectures and approximate for fixed in-degree. We demonstrate how
taking into account fluctuations in the linearization procedure increases the
accuracy of the effective theory and we explain the class dependent differences
between covariances in the time and the frequency domain. Finally we show that
the oscillatory instability emerging in networks of integrate-and-fire models
with delayed inhibitory feedback is a model-invariant feature: the same
structure of poles in the complex frequency plane determines the population
power spectra
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