Large scale multi-electrode recordings were used to measure electrical activity in nearly complete, regularly spaced mosaics of several hundred ON and OFF parasol (magnocellular-projecting) retinal ganglion cells (RGCs) in macaque monkey retina [Frechette et al, 2005]. The completeness of the mosaics indicates that we recorded from nearly every cell of both types in a 1x2 mm region of retina. In the presence of uniform, constant photopic illumination, pairs of RGCs fired synchronously (+/- 5 ms) much more often then expected by chance, indicating significant network interactions. Synchrony declined systematically with distance between cells, and differed for ON-ON, ON-OFF, and OFF-OFF pairs. These results provide strong constraints on the underlying circuitry, indicating that RGC connectivity is spatially localized and universal among cells of the same type.
However, this conventional pairwise analysis fails to distinguish whether synchrony arises only from pairwise interactions (e.g. reciprocal gap junctions) or instead reflects more complex interactions (e.g. diverging common input from presynaptic amacrine cells). This distinction is fundamental: diverging common input would be expected to produce very different multi-neuron firing patterns in RGCs than purely pairwise connections, and such firing patterns have been suggested as a mechanism for the retina to convey distinct, multiplexed visual messages to the brain [Meister 1995]. Furthermore, the spatial extent of synchrony may reflect signal spread through intermediate neurons, so pairwise analysis also fails to reveal the elementary spatial scale of network interactions. To test quantitatively whether network interactions are purely pairwise, and whether they are restricted to immediately adjacent neurons, requires a candidate null statistical model to compare against the observed data. In the simpler case of pairwise synchrony, the null model is statistical independence; but in a multi-cell circuit, many patterns of connectivity are consistent with the observed pairwise interactions. Therefore, we employ the maximum entropy framework to generate a null statistical model of firing patterns constrained by the observed pairwise correlations [Jaynes 1957, Schneidman et al 2003, 2006; Shlens et al 2006]. Borrowed from statistical mechanics, the maximum entropy approach has been employed in many fields of machine learning to determine a complete probabilistic model from overlapping constraints, without assuming additional statistical structure. We find that purely pairwise interactions account for >95% of the departures from statistical independence in parasol RGCs. Furthermore, the predictive ability of a pairwise model approaches the upper limits given the intrinsic reproducibility of the data. We also find that the more restricted model of pairwise interactions limited to adjacent neighbors in the mosaic also accounts for >98% of the departures from statistical independence, and approaches the intrinsic reproducibility of the data. Thus, multi-neuron firing patterns from populations of parasol cells can be understood as simply arising from reciprocal interactions between adjacent cells in the mosaic, suggestive of gap junction coupling between neighbors. This provides a dramatically simpler picture of retinal organization than has been proposed, and makes it possible to understand circuit activity with a relatively small number of measurements. We have begun to extend this approach to examine larger populations of RGCs as well as the presence of a stimulus.