410 research outputs found
Exact firing time statistics of neurons driven by discrete inhibitory noise
Neurons in the intact brain receive a continuous and irregular synaptic
bombardment from excitatory and inhibitory pre-synaptic neurons, which
determines the firing activity of the stimulated neuron. In order to
investigate the influence of inhibitory stimulation on the firing time
statistics, we consider Leaky Integrate-and-Fire neurons subject to inhibitory
instantaneous post-synaptic potentials. In particular, we report exact results
for the firing rate, the coefficient of variation and the spike train spectrum
for various synaptic weight distributions. Our results are not limited to
stimulations of infinitesimal amplitude, but they apply as well to finite
amplitude post-synaptic potentials, thus being able to capture the effect of
rare and large spikes. The developed methods are able to reproduce also the
average firing properties of heterogeneous neuronal populations.Comment: 20 pages, 8 Figures, submitted to Scientific Report
Synaptic shot noise and conductance fluctuations affect the membrane voltage with equal significance
The subthresholdmembranevoltage of a neuron in active cortical tissue is
a fluctuating quantity with a distribution that reflects the firing statistics
of the presynaptic population. It was recently found that conductancebased
synaptic drive can lead to distributions with a significant skew.
Here it is demonstrated that the underlying shot noise caused by Poissonian
spike arrival also skews the membrane distribution, but in the opposite
sense. Using a perturbative method, we analyze the effects of shot
noise on the distribution of synaptic conductances and calculate the consequent
voltage distribution. To first order in the perturbation theory, the
voltage distribution is a gaussian modulated by a prefactor that captures
the skew. The gaussian component is identical to distributions derived
using current-based models with an effective membrane time constant.
The well-known effective-time-constant approximation can therefore be
identified as the leading-order solution to the full conductance-based
model. The higher-order modulatory prefactor containing the skew comprises
terms due to both shot noise and conductance fluctuations. The
diffusion approximation misses these shot-noise effects implying that
analytical approaches such as the Fokker-Planck equation or simulation
with filtered white noise cannot be used to improve on the gaussian approximation.
It is further demonstrated that quantities used for fitting
theory to experiment, such as the voltage mean and variance, are robust
against these non-Gaussian effects. The effective-time-constant approximation
is therefore relevant to experiment and provides a simple analytic
base on which other pertinent biological details may be added
Decorrelation of neural-network activity by inhibitory feedback
Correlations in spike-train ensembles can seriously impair the encoding of
information by their spatio-temporal structure. An inevitable source of
correlation in finite neural networks is common presynaptic input to pairs of
neurons. Recent theoretical and experimental studies demonstrate that spike
correlations in recurrent neural networks are considerably smaller than
expected based on the amount of shared presynaptic input. By means of a linear
network model and simulations of networks of leaky integrate-and-fire neurons,
we show that shared-input correlations are efficiently suppressed by inhibitory
feedback. To elucidate the effect of feedback, we compare the responses of the
intact recurrent network and systems where the statistics of the feedback
channel is perturbed. The suppression of spike-train correlations and
population-rate fluctuations by inhibitory feedback can be observed both in
purely inhibitory and in excitatory-inhibitory networks. The effect is fully
understood by a linear theory and becomes already apparent at the macroscopic
level of the population averaged activity. At the microscopic level,
shared-input correlations are suppressed by spike-train correlations: In purely
inhibitory networks, they are canceled by negative spike-train correlations. In
excitatory-inhibitory networks, spike-train correlations are typically
positive. Here, the suppression of input correlations is not a result of the
mere existence of correlations between excitatory (E) and inhibitory (I)
neurons, but a consequence of a particular structure of correlations among the
three possible pairings (EE, EI, II)
Exact firing time statistics of neurons driven by discrete inhibitory noise
Neurons in the intact brain receive a continuous and irregular synaptic
bombardment from excitatory and inhibitory pre-synaptic neurons, which
determines the firing activity of the stimulated neuron. In order to
investigate the influence of inhibitory stimulation on the firing time
statistics, we consider Leaky Integrate-and-Fire neurons subject to
inhibitory instantaneous post-synaptic potentials. In particular, we report
exact results for the firing rate, the coefficient of variation and the spike
train spectrum for various synaptic weight distributions. Our results are not
limited to stimulations of infinitesimal amplitude, but they apply as well to
finite amplitude post-synaptic potentials, thus being able to capture the
effect of rare and large spikes. The developed methods are able to reproduce
also the average firing properties of heterogeneous neuronal populations
Exact analysis of the subthreshold variability for conductance-based neuronal models with synchronous synaptic inputs
The spiking activity of neocortical neurons exhibits a striking level of
variability, even when these networks are driven by identical stimuli. The
approximately Poisson firing of neurons has led to the hypothesis that these
neural networks operate in the asynchronous state. In the asynchronous state
neurons fire independently from one another, so that the probability that a
neuron experience synchronous synaptic inputs is exceedingly low. While the
models of asynchronous neurons lead to observed spiking variability, it is not
clear whether the asynchronous state can also account for the level of
subthreshold membrane potential variability. We propose a new analytical
framework to rigorously quantify the subthreshold variability of a single
conductance-based neuron in response to synaptic inputs with prescribed degrees
of synchrony. Technically we leverage the theory of exchangeability to model
input synchrony via jump-process-based synaptic drives; we then perform a
moment analysis of the stationary response of a neuronal model with all-or-none
conductances that neglects post-spiking reset. As a result, we produce exact,
interpretable closed forms for the first two stationary moments of the membrane
voltage, with explicit dependence on the input synaptic numbers, strengths, and
synchrony. For biophysically relevant parameters, we find that the asynchronous
regime only yields realistic subthreshold variability (voltage variance ) when driven by a restricted number of large synapses,
compatible with strong thalamic drive. By contrast, we find that achieving
realistic subthreshold variability with dense cortico-cortical inputs requires
including weak but nonzero input synchrony, consistent with measured pairwise
spiking correlations
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