A model of Weber and noise gain control in the retina of the toad Bufo marinus

We present several variations of a model of gain control in the retina of the toad Bufo marinus, and use them to fit the threshold-vs-intensity data of an actual toad ganglion cell [Donner et al. (1990). Journal of General Physiology, 95, 733-753]. Our models are based on a proposal by Donner et al. that the gain (neural spike per photon ratio) of toad ganglion cells is set by a sequence of two retinal gain control stages. The first stage consists of a Weber gain control mechanism at the level of the red rods. The second is a more proximal "noise gain" stage, which multiplies the (incremental) input signal by a factor that is inversely proportional to the standard deviation of the random ganglion cell input and, under conditions that produce the de Vries-Rose threshold law, is also proportional to the standard deviation of the photon fluctuations within the ganglion cell receptive field. We demonstrate that noise gain control arises naturally from modeling ganglion cell spike generation with either of two common types of spike generation models: integrate-and-fire models or threshold accommodation models. We simulate the process of spike generation in both types of models and show that either model can account for the basic overall shape of the toad t.v.i. curve. However, although integrate-and-fire models appropriately generate noise gain control, they cannot quantitatively fit the threshold data with realistic retinal parameters. Integrate-and-fire models also fail to account for the observed relationship between the generator potential of the ganglion cell and its spiking probability. A threshold accommodation model with realistic retinal parameters, on the other hand, can account for both the threshold data and the generator potential-spike probability relationship. When a Weber gain stage is added to the model at the photoreceptor level, the resulting two-stage gain control model is shown to account quantitatively for the ganglion cell t.v.i. curve of Bufo marinus over the full range of background levels studied by Donner et al.