Power-Law Input-Output Transfer Functions Explain the Contrast-Response and Tuning Properties of Neurons in Visual Cortex

Erez Persi,David Hansel,Pascal Barone,Carl Van Vreeswijk,Lionel Nowak,Peter E Latham

doi:10.1371/journal.pcbi.1001078

Abstract

We develop a unified model accounting simultaneously for the contrast invariance of the width of the orientation tuning curves (OT) and for the sigmoidal shape of the contrast response function (CRF) of neurons in the primary visual cortex (V1). We determine analytically the conditions for the structure of the afferent LGN and recurrent V1 inputs that lead to these properties for a hypercolumn composed of rate based neurons with a power-law transfer function. We investigate what are the relative contributions of single neuron and network properties in shaping the OT and the CRF. We test these results with numerical simulations of a network of conductance-based model (CBM) neurons and we demonstrate that they are valid and more robust here than in the rate model. The results indicate that because of the acceleration in the transfer function, described here by a power-law, the orientation tuning curves of V1 neurons are more tuned, and their CRF is steeper than those of their inputs. Last, we show that it is possible to account for the diversity in the measured CRFs by introducing heterogeneities either in single neuron properties or in the input to the neurons. We show how correlations among the parameters that characterize the CRF depend on these sources of heterogeneities. Comparison with experimental data suggests that both sources contribute nearly equally to the diversity of CRF shapes observed in V1 neurons.

Highlights

The dependence of the neuronal response amplitude on stimulus contrast, the contrast-response function (CRF), typically displays a sigmoidal shape in the visual cortex: it accelerates at low contrast and saturates at high contrast [1,2,3,4,5,6,7,8]
The question is: can one formulate, without resorting to synaptic depression, a model in which cortical neurons display contrast-invariant tuning-width for both membrane potential and spike responses, as in the feedforward model in the presence of synaptic noise, while at the same time intracortical interactions induce a saturation of the contrast response function (CRF) of cortical neurons at lower contrast than their LGN afferents ? To examine this question, we investigated a rate model of a hypercolumn in the visual cortex with neurons whose transfer function nonlinearity was described by a power-law
Our model consists of NE excitatory (E) and NI inhibitory (I) rate units with a power law input-output transfer function

Summary

Introduction

The dependence of the neuronal response amplitude on stimulus contrast, the contrast-response function (CRF), typically displays a sigmoidal shape in the visual cortex: it accelerates at low contrast and saturates at high contrast [1,2,3,4,5,6,7,8]. The membrane potential response of cortical neurons displays an orientation tuning width that is typically 1.5 times larger than that of the spiking response [15,26,27,28,29,30]. These contrast-invariant properties constitute strong constraints for understanding the mechanisms underlying the response of V1 neurons to visual stimuli

Methods

Results

Conclusion