Mathematical models for the spatial receptive-field organization of nonlagged X-cells in dorsal lateral geniculate nucleus of cat

Spatial receptive fields of relay cells in dorsal lateral geniculate nucleus (dLGN) have commonly been modeled as a difference of two Gaussian functions. We present alternative models for dLGN cells which take known physiological couplings between retina and dLGN and within dLGN into account. The models include excitatory input from a single retinal ganglion cell and feedforward inhibition via intrageniculate interneurons. Mathematical formulas describing the receptive field and response to circular spot stimuli are found both for models with a finite and an infinite number of ganglion-cell inputs to dLGN neurons. The advantage of these models compared to the common difference-of-Gaussians model is that they, in addition to providing mathematical descriptions of the receptive fields of dLGN neurons, also make explicit contributions from the geniculate circuit. Moreover, the model parameters have direct physiological relevance and can be manipulated and measured experimentally. The discrete model is applied to recently published data (Ruksenas et al., 2000) on response versus spot-diameter curves for dLGN cells and for the retinal input to the cell (S-potentials). The models are found to account well for the results for the X-cells in these experiments. Moreover, predictions from the discrete model regarding receptive-field sizes of interneurons, the amount of center-surround antagonism for interneurons compared to relay cells, and distance between neighboring retinal ganglion cells providing input to interneurons, are all compatible with data available in the literature.