# Modeling the impact of common noise inputs on the network activity of retinal ganglion cells

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## Abstract

Synchronized spontaneous firing among retinal ganglion cells (RGCs), on timescales faster than visual responses, has been reported in many studies. Two candidate mechanisms of synchronized firing include direct coupling and shared noisy inputs. In neighboring parasol cells of primate retina, which exhibit rapid synchronized firing that has been studied extensively, recent experimental work indicates that direct electrical or synaptic coupling is weak, but shared synaptic input in the absence of modulated stimuli is strong. However, previous modeling efforts have not accounted for this aspect of firing in the parasol cell population. Here we develop a new model that incorporates the effects of common noise, and apply it to analyze the light responses and synchronized firing of a large, densely-sampled network of over 250 simultaneously recorded parasol cells. We use a generalized linear model in which the spike rate in each cell is determined by the linear combination of the spatio-temporally filtered visual input, the temporally filtered prior spikes of that cell, and unobserved sources representing common noise. The model accurately captures the statistical structure of the spike trains and the encoding of the visual stimulus, without the direct coupling assumption present in previous modeling work. Finally, we examined the problem of decoding the visual stimulus from the spike train given the estimated parameters. The common-noise model produces Bayesian decoding performance as accurate as that of a model with direct coupling, but with significantly more robustness to spike timing perturbations.

## Keywords

Retina Generalized linear model State-space model Multielectrode Recording Random-effects model## Notes

### Acknowledgements

We would like to thank F. Rieke for helpful suggestions and insight; K. Masmoudi for bringing the analogy to the dithering process to our attention; O. Barak, X. Pitkow and M. Greschner for comments on the manuscript; G. D. Field, J. L. Gauthier, and A. Sher for experimental assistance. A preliminary version of this work was presented in Vidne et al. (2009). In addition, an early version of Fig. 2 appeared previously in the review paper (Paninski et al. 2010), and Fig. 11(D) is a reproduction of a schematic figure from (Shlens et al. 2006). This work was supported by: the Gatsby Foundation (M.V.); a Robert Leet and Clara Guthrie Patterson Trust Postdoctoral Fellowship (Y.A.); an NSF Integrative Graduate Education and Research Traineeship Training Grant DGE-0333451 and a Miller Institute Fellowship for Basic Research in Science, UC Berkeley (J.S.); US National Science Foundation grant PHY-0417175 (A.M.L.); NIH Grant EY017736 (E.J.C.); HHMI (E.P.S.); NEI grant EY018003 (E.J.C., L.P. and E.P.S.); and a McKnight Scholar award (L.P.). We also gratefully acknowledge the use of the Hotfoot shared cluster computer at Columbia University.

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