Characterizing the nonlinear subunits of primate retinal ganglion cells

J Freeman, G D Field, P H Li, M Greschner, L H Jepson, N C Rabinowitz, E Pnevmatikakis, D E Gunning, K Mathieson, A M Litke, E J Chichilnisky, L Paninski and E P Simoncelli

Published in Annual Meeting, Neuroscience, Oct 2012.

This paper has been superseded by:
Mapping nonlinear receptive field subunits in primate retina at single cone resolution
J Freeman, G D Field, P H Li, M Greschner, D H Gunning, K Mathieson, A Sher, A M Litke, L Paninski, E P Simoncelli and E J Chichilnisky.
eLife, vol.4:e05241 Oct 2015.

Hierarchical cascades of linear and nonlinear processing are ubiquitous computational motifs in neural circuits and artificial vision. In primate vision, such computations begin in the retina. Several types of retinal ganglion cells (RGCs) exhibit nonlinear responses to spatially-structured stimuli that can be explained by the existence of "subunits" within the receptive field - small, localized filters with rectifying output nonlinearities (Hochstein and Shapley, 1976). These subunits are hypothesized to reflect the function of bipolar cells that convey cone signals to RGCs.

Here, we present a novel approach to characterize the flow of visual signals from cones through nonlinear subunits to RGCs. Extracellular multi-electrode recordings were obtained from RGCs in isolated primate retina. High-resolution white noise stimuli were used to stimulate individual cones within each RGC receptive field. To explore subunit nonlinearities, RGC responses were fitted with a model consisting of two linear-nonlinear stages. The first stage was a collection of subunits that weight and sum signals from small groups of cones followed by a nonlinearity. The second stage was a weighted sum of subunit responses followed by a final output nonlinearity. Fitting such a model involves inferring the connectivity between cones and subunits, and estimating the associated weights and nonlinearities at both stages. To infer connectivity, we developed a conditional measure of the degree of linear vs. nonlinear interaction between pairs of cones, and applied graph analysis (clique finding and spectral clustering) to the pairwise measures. Maximum likelihood estimates of weights at both stages, as well as a cubic spline parameterization of the subunit nonlinearity, were obtained using block coordinate ascent.

Fitted subunits for both midget (parvocellular-projecting) and parasol (magnocellular-projecting) RGCs revealed nonlinearities with varying degrees of rectification. Midget subunits included 1-3 cones, consistent with anatomical convergence of cones to midget bipolar cells. Parasol subunits exhibited greater cone convergence, also approximately consistent with anatomical data. The model explained more variance (typically 10-20%, at most 30-40%) in responses to white noise than a simple linear-nonlinear model, and the structure of the model points to new classes of stimuli that can further amplify this difference. The improvement in explained variance is comparable to results achieved using spike-triggered covariance analysis, but the structure and parameters of the model are more readily interpreted in terms of the underlying circuitry.

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