(A) The reduced version of the model (right) produces qualitatively similar curves of response vs. stimulus strength

*c* as the full model (left; for the full model, this is the response of the cells at θ = 0°). The top plots show the response curves for a stimulus composed of a single grating with orientation θ = 0° and the bottom plots show the response for a two-grating stimulus composed of the grating at θ = 0° and a grating at θ = 90°. In the 2-D reduced model, these two cases are represented by using Ψ = 0.774 for one grating and Ψ = 1.024 for two gratings (see for the definition of Ψ and the text after for the method we used to calculate these values). (B) Full and reduced models show a similar stimulus-strength-dependent transition from supralinear summation (weight > 1) to sublinear summation (weight < 1) of the responses to two gratings, where the weight

*w* is defined as follows. For the full model, for either E or I cells, we let

*R*_{1}(θ),

*R*_{2}(θ), and

*R*_{12}(θ) be the response to one grating, the other grating, or the superposition of the two, and we define

, where θ = 0 is the orientation of the first grating. For the reduced model, we define the weight as

, where

*R*_{1}, and

*R*_{12} are the responses to one or two gratings (modeled by the two values of Ψ given above) and we set

*R*_{2} = 0 (by the way we defined the reduction,

*R*_{1},

*R*_{2} and

*R*_{12} should approximate the responses of the full model at θ = 0). (C) Full and reduced models have nearly identical stimulus-strength-dependent tuning for the width in orientation, σ

_{stim}, of a feedforward stimulus (full model: width of Gaussian stimulus centered at θ = 0 with given stimulus strength

*c* that gives the strongest response in cells at θ = 0; reduced model: Ψ is computed for each stimulus width as described in the text after , and plot shows width whose Ψ gives maximal response). In all curves, red shows E cells and blue shows I cells. All responses are steady-state responses. Full model solutions found by simulating until convergence to steady state. Parameters:

*J*_{EE} = 2.5,

*J*_{IE} = 2.4,

*J*_{EI} = 1.3,

*J*_{II} = 1.0, τ

_{E} = 20 m

*s*, τ

_{I} = 10 m

*s*,

*k* = 0.04,

*n* = 2.0, σ

_{ori} = 32°; σ

_{stim} = 30° in A,B.

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