Contrast-dependent nonlinearities arise locally in a model of contrast-invariant orientation tuning

We study a recently proposed correlation-based, push-pull model of the circuitry of layer 4 of cat visual cortex. This model was previously shown to explain the contrast-invariance of cortical orientation tuning. Here we show that it can simultaneously account for several contrast-dependent (c-d) nonlinearities in cortical responses. These include an advance with increasing contrast in the temporal phase of response to a sinusoidally modulated stimulus; a change in shape of the temporal frequency tuning curve, so that higher temporal frequencies may give little or no response at low contrast but reasonable responses at high contrast; and contrast saturation that occurs at lower contrasts in cortex than in the lateral geniculate nucleus (LGN). In the context of the model circuit, these properties arise from a mixture of nonlinear cellular and synaptic mechanisms: short-term synaptic depression, spike-rate adaptation, contrast-induced changes in cellular conductance, and the nonzero spike threshold. The former three mechanisms are sufficient to explain the experimentally observed increase in c-d phase advance in cortex relative to LGN. The c-d changes in temporal frequency tuning arise as a threshold effect: voltage modulations in response to higher-frequency inputs are only slightly above threshold at lower contrast, but become robustly suprathreshold at higher contrast. The other three nonlinear mechanisms also play a crucial role in this result, allowing contrast dependence of temporal frequency tuning to coexist with contrast-invariance of orientation tuning. Contrast saturation, and the observation that responses to stimuli of increasing temporal frequency saturate at increasingly high contrasts, can be induced both by the model's push-pull inhibition and by synaptic depression. Previous proposals explained these nonlinear response properties by assuming contrast-invariant orientation tuning as a starting point, and adding normalization by shunting inhibition derived equally from cells of all preferred orientations. The present proposal simultaneously explains both contrast-invariant orientation tuning and these contrast-dependent nonlinearities and requires only processing that is local in orientation, in agreement with intracellular measurements.