Predicting neuronal dynamics with a delayed gain control model
Fig 2
The delayed normalization (DN) model.
(A) The input to the model is the contrast time course of a stimulus, S, which is 0 when the stimulus is absent and 1 when it is present. First, the model computes the linear neuronal response by convolving S with an impulse response function h1 (parameterized by τ1 and w). The linear output is then full-wave rectified and exponentiated by n. We assumed n>1 in this paper. The exponentiated output is divisively normalized by a denominator that consists of two components: a semi-saturation constant (σ), and a causally low-pass filtered version of the driving signal. Both components were raised to the same power n. The predicted neuronal response (right) to the example input stimulus S (left) includes a transient followed by a lower-level, more sustained response. (B) The effects of varying each of the 5 parameters are shown. For example, larger w means a more biphasic impulse response, therefore a larger transient response at stimulus offset (top row). In all simulations, the default parameters are w = 0, τ1 = 0.05, τ2 = 0.1, n = 2, σ = 1. For more details of model behavior see S1 Fig.