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SummaryWhen stimulated, neural populations in the visual cortex exhibit fast rhythmic activity with frequencies in the gamma band (30-80 Hz). The gamma rhythm manifests as a broad resonance peak in the powerspectrum of recorded local field potentials, which exhibits various stimulus dependencies. In particular, in macaque primary visual cortex (V1), the gamma peak frequency increases with increasing stimulus contrast. Moreover, this contrast dependence is local: when contrast varies smoothly over visual space, the gamma peak frequency in each cortical column is controlled by the local contrast in that column’s receptive field. No parsimonious mechanistic explanation for these contrast dependencies of V1 gamma oscillations has been proposed. The stabilized supralinear network (SSN) is a mechanistic model of cortical circuits that has accounted for a range of visual cortical response nonlinearities and contextual modulations, as well as their contrast dependence. Here, we begin by showing that a reduced SSN model without retinotopy robustly captures the contrast dependence of gamma peak frequency, and provides a mechanistic explanation for this effect based on the observed non-saturating and supralinear input-output function of V1 neurons. Given this result, the local dependence on contrast can trivially be captured in a retinotopic SSN which however lacks horizontal synaptic connections between its cortical columns. However, long-range horizontal connections in V1 are in fact strong, and underlie contextual modulation effects such as surround suppression. We thus explored whether a retinotopically organized SSN model of V1 with strong excitatory horizontal connections can exhibit both surround suppression and the local contrast dependence of gamma peak frequency. We found that retinotopic SSNs can account for both effects, but only when the horizontal excitatory projections are composed of two components with different patterns of spatial fall-off with distance: a short-range component that only targets the source column, combined with a long-range component that targets columns neighboring the source column. We thus make a specific qualitative prediction for the spatial structure of horizontal connections in macaque V1, consistent with the columnar structure of cortex.

Neural responses to a localized visual stimulus are modulated by the content of its surrounding. This phenomenon manifests in several forms of contextual modulation, including three interrelated properties of the visual cortex: surround suppression, inverse response and surround facilitation. We devise a unified biologically realistic circuit model accounting for all these phenomena and show that i) surround suppression in L2/3 is only partially due to the recruitment of lateral inhibition; ii) long-range feedback projections are necessary for inverse response and iii) the width of the response profile in the feedback layer determines inverse size tuning. The model predicts the modulations induced by silencing somatostatin-expressing cells or higher visual areas or changing the stimulus contrast. These predictions are consistent with the experimental observations when available and can be tested in existing setups otherwise. We then show the robustness of the identified mechanisms in a model with three interneuron subclasses, built to fit the classical responses and able to predict inverse size-tuning curves.HighlightsOne model explains three different types of contextual modulation: (classical) surround suppression, (inverse) response to ‘holes’ in full field drifting gratings and cross orientation surround facilitation.Feedback, feedforward and lateral inhibitory inputs contribute to classical surround suppression in L2/3 of mouse V1 in different amounts.Observed responses to ‘holes’ in full field drifting gratings require long-range feedback projections.Surround modulation to the response to ‘holes’ in full field drifting gratings requires an increase in the characteristic length scale of the spatial pattern of activity in higher visual areas.The mechanisms uncovered by an analytically tractable model are also at work in a cell-type specific model that predicts response to a ‘hole’ stimulus.