Abstract
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.
Highlights
Neurons in the neocortex in vivo are subject to a continuous synaptic bombardment reflecting the intense network activity[1]
We will apply the developed formalism to estimate the response of a single leaky integrate-and-fire (LIF) neuron as well as the firing characteristics of a sparse inhibitory neural network for different synaptic weight distributions
The firing time statistics of a neuron subject to a noisy uncorrelated input is theoretically estimated within the DA3, 4, 29
Summary
Neurons in the neocortex in vivo are subject to a continuous synaptic bombardment reflecting the intense network activity[1]. In the so-called high-input regime, in which neurons receive hundreds of synaptic inputs during each interspike interval[2], the firing statistics of model neurons is usually obtained in the context of the diffusion approximation (DA)[3, 4] Within such an approximation the post-synaptic potentials (PSPs) are assumed to have small amplitudes and high arrival rates, the synaptic inputs can be treated as a continuous stochastic process characterized by its average and variance, while the shape of the distribution of the amplitudes of the PSPs is irrelevant[5]. We estimate the firing time statistics for LIF neurons subject to inhibitory post-synaptic potentials (IPSPs)
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