How noise contributes to contrast invariance of orientation tuning

David Hansel and Carl van Vreeswijk

Laboratoire de Neurophysique et Physiologie du Systeme Moteur

Remarkably, the orientation tuning curves of the spike response of neurons in V1 is invariant to contrast (Sclar and Freeman, 1982; Skottun et al. 1987). In a recent paper Anderson et al. (Anderson et al. 2000) have shown that contrast invariance is also displayed by the tuning curves of the membrane potential of these neurons. They also demonstrated that voltage responses to visual stimuli of neurons in V1 are on average subthreshold, the spike response being driven by a strong noise. Anderson et al. proposed that although the iceberg effect prevents the spike response from being contrast invariant, trial by trial, averaging over trials restores this invariance. This idea was tested by numerical simulations of a neuronal model in which spikes are generated from the mean voltage through the addition of Gaussian noise, followed by a threshold-linear transfer to the output rate.

In this poster we study analytically the model of Anderson et al. We explain how the proposed mechanism works. We derive the required conditions to get this invariance. In particular we find that it can only be approximate, that it requires that the neuron firing rate is not too large and that increasing or lowering the contrast too much destroys it. There is also an upper and lower limit for the noise variance. Within these constraints, the mechanism is quite general. Neither the threshold linearity of the transfer function, nor the Gaussianity of the added noise, are crucial.

This is confirmed by a further analytical study which uses an integrate and fire neuron receiving tuned input with added Gaussian noise, and numerical simulations of a conductance based neuron that receives Poissonian synaptic inputs. In these two models we assume that the input is contrast invariant. With an appropriate setting of the noise, this input contrast invariance results in an approximate contrast invariance for the mean voltage as well as the mean firing rate.

We also show that, if this mechanism operates in V1, the spike response, r, and voltage response v of the neurons in V1 should vary with the contrast, C, according to r(C) ~ v(C)a, where a can be estimated from the amount by which the spike tuning curve is sharpened with respect to the voltage tuning curves of the neurons. This prediction does not depends on the details of the model, and can easily be checked experimentally.