1,006 research outputs found
Intrinsic gain modulation and adaptive neural coding
In many cases, the computation of a neural system can be reduced to a
receptive field, or a set of linear filters, and a thresholding function, or
gain curve, which determines the firing probability; this is known as a
linear/nonlinear model. In some forms of sensory adaptation, these linear
filters and gain curve adjust very rapidly to changes in the variance of a
randomly varying driving input. An apparently similar but previously unrelated
issue is the observation of gain control by background noise in cortical
neurons: the slope of the firing rate vs current (f-I) curve changes with the
variance of background random input. Here, we show a direct correspondence
between these two observations by relating variance-dependent changes in the
gain of f-I curves to characteristics of the changing empirical
linear/nonlinear model obtained by sampling. In the case that the underlying
system is fixed, we derive relationships relating the change of the gain with
respect to both mean and variance with the receptive fields derived from
reverse correlation on a white noise stimulus. Using two conductance-based
model neurons that display distinct gain modulation properties through a simple
change in parameters, we show that coding properties of both these models
quantitatively satisfy the predicted relationships. Our results describe how
both variance-dependent gain modulation and adaptive neural computation result
from intrinsic nonlinearity.Comment: 24 pages, 4 figures, 1 supporting informatio
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
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
Time Resolution Dependence of Information Measures for Spiking Neurons: Atoms, Scaling, and Universality
The mutual information between stimulus and spike-train response is commonly
used to monitor neural coding efficiency, but neuronal computation broadly
conceived requires more refined and targeted information measures of
input-output joint processes. A first step towards that larger goal is to
develop information measures for individual output processes, including
information generation (entropy rate), stored information (statistical
complexity), predictable information (excess entropy), and active information
accumulation (bound information rate). We calculate these for spike trains
generated by a variety of noise-driven integrate-and-fire neurons as a function
of time resolution and for alternating renewal processes. We show that their
time-resolution dependence reveals coarse-grained structural properties of
interspike interval statistics; e.g., -entropy rates that diverge less
quickly than the firing rate indicate interspike interval correlations. We also
find evidence that the excess entropy and regularized statistical complexity of
different types of integrate-and-fire neurons are universal in the
continuous-time limit in the sense that they do not depend on mechanism
details. This suggests a surprising simplicity in the spike trains generated by
these model neurons. Interestingly, neurons with gamma-distributed ISIs and
neurons whose spike trains are alternating renewal processes do not fall into
the same universality class. These results lead to two conclusions. First, the
dependence of information measures on time resolution reveals mechanistic
details about spike train generation. Second, information measures can be used
as model selection tools for analyzing spike train processes.Comment: 20 pages, 6 figures;
http://csc.ucdavis.edu/~cmg/compmech/pubs/trdctim.ht
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
Effective long-time phase dynamics of limit-cycle oscillators driven by weak colored noise
An effective white-noise Langevin equation is derived that describes
long-time phase dynamics of a limit-cycle oscillator subjected to weak
stationary colored noise. Effective drift and diffusion coefficients are given
in terms of the phase sensitivity of the oscillator and the correlation
function of the noise, and are explicitly calculated for oscillators with
sinusoidal phase sensitivity functions driven by two typical colored Gaussian
processes. The results are verified by numerical simulations using several
types of stochastic or chaotic noise. The drift and diffusion coefficients of
oscillators driven by chaotic noise exhibit anomalous dependence on the
oscillator frequency, reflecting the peculiar power spectrum of the chaotic
noise.Comment: 16 pages, 6 figure
Motif Statistics and Spike Correlations in Neuronal Networks
Motifs are patterns of subgraphs of complex networks. We studied the impact
of such patterns of connectivity on the level of correlated, or synchronized,
spiking activity among pairs of cells in a recurrent network model of integrate
and fire neurons. For a range of network architectures, we find that the
pairwise correlation coefficients, averaged across the network, can be closely
approximated using only three statistics of network connectivity. These are the
overall network connection probability and the frequencies of two second-order
motifs: diverging motifs, in which one cell provides input to two others, and
chain motifs, in which two cells are connected via a third intermediary cell.
Specifically, the prevalence of diverging and chain motifs tends to increase
correlation. Our method is based on linear response theory, which enables us to
express spiking statistics using linear algebra, and a resumming technique,
which extrapolates from second order motifs to predict the overall effect of
coupling on network correlation. Our motif-based results seek to isolate the
effect of network architecture perturbatively from a known network state
Low-dimensional firing-rate dynamics for populations of renewal-type spiking neurons
The macroscopic dynamics of large populations of neurons can be
mathematically analyzed using low-dimensional firing-rate or neural-mass
models. However, these models fail to capture spike synchronization effects of
stochastic spiking neurons such as the non-stationary population response to
rapidly changing stimuli. Here, we derive low-dimensional firing-rate models
for homogeneous populations of general renewal-type neurons, including
integrate-and-fire models driven by white noise. Renewal models account for
neuronal refractoriness and spike synchronization dynamics. The derivation is
based on an eigenmode expansion of the associated refractory density equation,
which generalizes previous spectral methods for Fokker-Planck equations to
arbitrary renewal models. We find a simple relation between the eigenvalues,
which determine the characteristic time scales of the firing rate dynamics, and
the Laplace transform of the interspike interval density or the survival
function of the renewal process. Analytical expressions for the Laplace
transforms are readily available for many renewal models including the leaky
integrate-and-fire model. Retaining only the first eigenmode yields already an
adequate low-dimensional approximation of the firing-rate dynamics that
captures spike synchronization effects and fast transient dynamics at stimulus
onset. We explicitly demonstrate the validity of our model for a large
homogeneous population of Poisson neurons with absolute refractoriness, and
other renewal models that admit an explicit analytical calculation of the
eigenvalues. The here presented eigenmode expansion provides a systematic
framework for novel firing-rate models in computational neuroscience based on
spiking neuron dynamics with refractoriness.Comment: 24 pages, 7 figure
Feature selection in simple neurons: how coding depends on spiking dynamics
The relationship between a neuron's complex inputs and its spiking output
defines the neuron's coding strategy. This is frequently and effectively
modeled phenomenologically by one or more linear filters that extract the
components of the stimulus that are relevant for triggering spikes, and a
nonlinear function that relates stimulus to firing probability. In many sensory
systems, these two components of the coding strategy are found to adapt to
changes in the statistics of the inputs, in such a way as to improve
information transmission. Here, we show for two simple neuron models how
feature selectivity as captured by the spike-triggered average depends both on
the parameters of the model and on the statistical characteristics of the
input.Comment: 23 Pages, LaTeX + 4 Figures. v2 is substantially expanded and
revised. v3 corrects minor errors in Sec. 3.
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