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

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.Author Summary: Both the response and membrane potential of neurons in the primary visual cortex (V1) are selective to the orientation of elongated stimuli. The widths of the tuning curves, which characterize this selectivity, hardly depend on stimulus contrast whereas their amplitude does. The contrast dependence of this amplitude, the contrast response function (CRF), has a sigmoidal shape. Saturation of the spike response is substantially lower than the neurons' maximal firing rate. These well established facts constrain the possible mechanisms for orientation selectivity in V1. Furthermore, the single neuron CRFs in V1 display a broad diversity in their shape. This adds other constraints. Many theoretical works have tried to elaborate mechanisms of orientation selectivity that are compatible with the contrast invariant tuning widths. However, these mechanisms are usually incompatible with sigmoidal CRFs. We propose a mechanism which accounts simultaneously for contrast invariant tuning width for both rate and voltage response and for the shape and diversity of the CRFs. This mechanism relies on the interplay between power-law frequency-current transfer functions of single neurons, as measured in vivo in cortex, and on the recurrent interactions in the cortical circuit.