  The retina is the entrance of the visual system. Although based on common
biophysical principles the dynamics of retinal neurons is quite different from
their cortical counterparts, raising interesting problems for modellers. In
this paper I address some mathematically stated questions in this spirit,
discussing, in particular: (1) How could lateral amacrine cell connectivity
shape the spatio-temporal spike response of retinal ganglion cells ? (2) How
could spatio-temporal stimuli correlations and retinal network dynamics shape
the spike train correlations at the output of the retina ? These questions are
addressed, first, introducing a mathematically tractable model of the layered
retina, integrating amacrine cells lateral connectivity and piecewise linear
rectification, allowing to compute the retinal ganglion cells receptive field
together with the voltage and spike correlations of retinal ganglion cells
resulting from the amacrine cells networks. Then, I review some recent results
showing how the concept of spatio-temporal Gibbs distributions and linear
response theory can be used to characterize the collective spike response to a
spatio-temporal stimulus of a set of retinal ganglion cells, coupled via
effective interactions corresponding to the amacrine cells network. On these
bases, I briefly discuss several potential consequences of these results at the
cortical level.
