Response Variability in Balanced Cortical Networks

Abstract

We study the spike statistics of neurons in a network with dynamically balanced excitation and inhibition. Our model, intended to represent a generic cortical column, comprises randomly connected excitatory and inhibitory leaky integrate-and-fire neurons, driven by excitatory input from an external population. The high connectivity permits a mean-field description in which synaptic currents can be treated as Gaussian noise, the mean and autocorrelation function of which are calculated self-consistently from the firing statistics of single model neurons. Within this description, we find that the irregularity of spike trains is controlled mainly by the strength of the synapses relative to the difference between the firing threshold and the post-firing reset level of the membrane potential. For moderately strong synapses we find spike statistics very similar to those observed in primary visual cortex.

Mean field theory for a balanced hypercolumn model of orientation selectivity in primary visual cortex

“…How to do this correctly was first shown for an all-inhibitory network by Hertz et al [7] using the systematic formulation of mean field theory due to Fulvi Mari [8]. In a recent paper [9] we presented a mean-field theory for a balanced network model that allowed us to quantify how the irregularity in firing and, more generally, the firing correlations depend on intrinsic network properties such as synaptic strengths. The analysis was applied to a statistically homogeneous network, representing a cortical column composed of neurons with similar response characteristics.…”

“…However, the formulation is general enough to allow for non-stationary rates. We presented such a time-dependent treatment for a balanced single-column model elsewhere [9]. Because of the dilute random connectivity, each neuron receives a high number of uncorrelated inputs (we assume K b to be large, but smaller than N b ).…”

Slow fluctuations in recurrent networks of spiking neurons

“…Both the rate and spectrum can be approximately determined in a single-neuron simulation scheme of Eq. (3), in which iteratively a single neuron is stimulated over several "generations" with surrogate Gaussian noise, the power spectrum of which matches the previous generation's spike-train spectrum [20,21]. Formally, we iterate a functional map M that leads from the rate and spectrum of the nth generation to those of the (n + 1)th, (r 0 ,S xx ) n+1 = M[(r 0 ,S xx ) n ]-the fixed point of this map yields the self-consistent solution.…”

Mean Field Methods for Cortical Network Dynamics

“…where I a (t) is given by (2). (We have dropped the neuron index i, since we are now doing a one-neuron problem.)…”

“…We have to start with a guess about the mean rates, the rate fluctuations, and the correlation functions for the neurons in the two populations. We then generate noise according to (2) and simulate many trials of neurons driven by realizations of this noise. In these trials, the effective numbers of inputs K b are varied randomly from trial to trial, with a Gaussian distribution of width √ K b , to capture the effects of the random connectivity in the network.…”