Modeling lateral geniculate nucleus response with contrast gain control. Part 2: analysis.

Cope et al. [J. Opt. Soc. Am. A30, 2401 (2013)] proposed a class of models for lateral geniculate nucleus (LGN) ON-cell behavior consisting of a linear response with divisive normalization by local stimulus contrast. Here, we analyze a specific model with the linear response defined by a difference-of-Gaussians filter, and a circular Gaussian for the gain pool weighting function. For sinusoidal grating stimuli, the parameter region for bandpass behavior of the linear response is determined, and the gain control response is shown to act as a switch (changing from "off" to "on" with increasing spatial frequency). It is also shown that large gain pools stabilize the optimal spatial frequency of the total nonlinear response at a fixed value independent of contrast and stimulus magnitude. Under- and super-saturation, as well as contrast saturation, occur as typical effects of stimulus magnitude. For circular spot stimuli, it is shown that large gain pools stabilize the spot size that yields the maximum response.