Stochastic neural field model of stimulus-dependent variability in cortical neurons.

Paul C Bressloff,Bard G Ermentrout

doi:10.1371/journal.pcbi.1006755

Abstract

We use stochastic neural field theory to analyze the stimulus-dependent tuning of neural variability in ring attractor networks. We apply perturbation methods to show how the neural field equations can be reduced to a pair of stochastic nonlinear phase equations describing the stochastic wandering of spontaneously formed tuning curves or bump solutions. These equations are analyzed using a modified version of the bivariate von Mises distribution, which is well-known in the theory of circular statistics. We first consider a single ring network and derive a simple mathematical expression that accounts for the experimentally observed bimodal (or M-shaped) tuning of neural variability. We then explore the effects of inter-network coupling on stimulus-dependent variability in a pair of ring networks. These could represent populations of cells in two different layers of a cortical hypercolumn linked via vertical synaptic connections, or two different cortical hypercolumns linked by horizontal patchy connections within the same layer. We find that neural variability can be suppressed or facilitated, depending on whether the inter-network coupling is excitatory or inhibitory, and on the relative strengths and biases of the external stimuli to the two networks. These results are consistent with the general observation that increasing the mean firing rate via external stimuli or modulating drives tends to reduce neural variability.

Highlights

A growing number of experimental studies have investigated neural variability across a variety of cortical areas, brain states and stimulus conditions [1,2,3,4,5,6,7,8,9,10,11]
Since trial-by-trial variability and noise correlations are known to affect the information capacity of neurons, such suppression could improve the accuracy of population codes
In this paper we show how the stimulus-dependent tuning of neural variability in ring attractor networks can be analyzed in terms of the stochastic wandering of spontaneously formed tuning curves or bumps in a continuum neural field model

Summary

Introduction

A growing number of experimental studies have investigated neural variability across a variety of cortical areas, brain states and stimulus conditions [1,2,3,4,5,6,7,8,9,10,11]. Ponce-Alvarez et al [10] examined the in vivo statistical responses of direction selective area-middle temporal (MT) neurons to moving gratings and plaid patterns. They determined the baseline levels and the evoked directional and contrast tuning of the variance of individual neurons and the noise correlations between pairs of neurons with similar direction preferences. The authors computationally explored the effect of an applied stimulus on variability and correlations in a stochastic ring network model of direction selectivity They found experimentally that both the trial-by-trial variability and the noise correlations among MT neurons were suppressed by an external stimulus and exhibited bimodal directional tuning. These results could be reproduced in a stochastic ring model, provided that the latter operated close to or beyond the bifurcation point for the existence of spontaneous bump solutions

Methods

Results

Discussion

Conclusion