Abstract
The output of the retina is organized into many detector grids, called ‘mosaics’, that signal different features of visual scenes to the brain1,2,3,4. Each mosaic comprises a single type of retinal ganglion cell (RGC), whose receptive fields tile visual space. Many mosaics arise as pairs, signalling increments (ON) and decrements (OFF), respectively, of a particular visual feature5. Here we use a model of efficient coding6 to determine how such mosaic pairs should be arranged to optimize the encoding of natural scenes. We find that information is maximized when these mosaic pairs are anti-aligned, meaning that the distances between the receptive field centres across mosaics are greater than expected by chance. We tested this prediction across multiple receptive field mosaics acquired using large-scale measurements of the light responses of rat and primate RGCs. ON and OFF RGC pairs with similar feature selectivity had anti-aligned receptive field mosaics, consistent with this prediction. ON and OFF RGC types that encode distinct features have independent mosaics. These results extend efficient coding theory beyond individual cells to predict how populations of diverse types of RGC are spatially arranged.
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Data availability
Raw data will be made available upon request. Source data are provided with this paper.
Code availability
Analysis code is available at https://doi.org/10.5281/zenodo.4441277.
References
Devries, S. H. & Baylor, D. A. Mosaic arrangement of ganglion cell receptive fields in rabbit retina. J. Neurophysiol. 78, 2048–2060 (1997).
Field, G. D. & Chichilnisky, E. J. Information processing in the primate retina: circuitry and coding. Annu. Rev. Neurosci. 30, 1–30 (2007).
Wässle, H., Peichl, L. & Boycott, B. B. Dendritic territories of cat retinal ganglion cells. Nature 292, 344–345 (1981).
Wässle, H., Peichl, L. & Boycott, B. B. Morphology and topography of on- and off-alpha cells in the cat retina. Proc. R. Soc. Lond. B Biol. Sci. 212, 157–175 (1981).
Callaway, E. M. Structure and function of parallel pathways in the primate early visual system. J. Physiol. (Lond.) 566, 13–19 (2005).
Karklin, Y. & Simoncelli, E. P. Efficient coding of natural images with a population of noisy linear-nonlinear neurons. Adv. Neural Inf. Process. Syst. 24, 999–1007 (2011).
Bae, J. A. et al. Digital museum of retinal ganglion cells with dense anatomy and physiology. Cell 173, 1293–1306.e19 (2018).
Borghuis, B. G., Ratliff, C. P., Smith, R. G., Sterling, P. & Balasubramanian, V. Design of a neuronal array. J. Neurosci. 28, 3178–3189 (2008).
Gjorgjieva, J., Sompolinsky, H. & Meister, M. Benefits of pathway splitting in sensory coding. J. Neurosci. 34, 12127–12144 (2014).
Ratliff, C. P., Borghuis, B. G., Kao, Y. H., Sterling, P. & Balasubramanian, V. Retina is structured to process an excess of darkness in natural scenes. Proc. Natl Acad. Sci. USA 107, 17368–17373 (2010).
Jang, J. & Paik, S. B. Interlayer repulsion of retinal ganglion cell mosaics regulates spatial organization of functional maps in the visual cortex. J. Neurosci. 37, 12141–12152 (2017).
Kremkow, J., Jin, J., Wang, Y. & Alonso, J. M. Principles underlying sensory map topography in primary visual cortex. Nature 533, 52–57 (2016).
Lee, K. S., Huang, X. & Fitzpatrick, D. Topology of ON and OFF inputs in visual cortex enables an invariant columnar architecture. Nature 533, 90–94 (2016).
Mazade, R., Jin, J., Pons, C. & Alonso, J. M. Functional specialization of ON and OFF cortical pathways for global-slow and local-fast vision. Cell Rep. 27, 2881–2894.e5 (2019).
Rockhill, R. L., Euler, T. & Masland, R. H. Spatial order within but not between types of retinal neurons. Proc. Natl Acad. Sci. USA 97, 2303–2307 (2000).
Wässle, H., Boycott, B. B. & Illing, R. B. Morphology and mosaic of on- and off-beta cells in the cat retina and some functional considerations. Proc. R. Soc. Lond. B Biol. Sci. 212, 177–195 (1981).
Brown, S. P., He, S. & Masland, R. H. Receptive field microstructure and dendritic geometry of retinal ganglion cells. Neuron 27, 371–383 (2000).
Doi, E. et al. Efficient coding of spatial information in the primate retina. J. Neurosci. 32, 16256–16264 (2012).
Galli-Resta, L., Novelli, E., Kryger, Z., Jacobs, G. H. & Reese, B. E. Modelling the mosaic organization of rod and cone photoreceptors with a minimal-spacing rule. Eur. J. Neurosci. 11, 1461–1469 (1999).
Eglen, S. J., Diggle, P. J. & Troy, J. B. Homotypic constraints dominate positioning of on- and off-center beta retinal ganglion cells. Vis. Neurosci. 22, 859–871 (2005).
Eglen, S. J. Development of regular cellular spacing in the retina: theoretical models. Math. Med. Biol. 23, 79–99 (2006).
Dabrowski, W., Grybos, P. & Litke, A. M. A low noise multichannel integrated circuit for recording neuronal signals using microelectrode arrays. Biosens. Bioelectron. 19, 749–761 (2004).
Ravi, S., Ahn, D., Greschner, M., Chichilnisky, E. J. & Field, G. D. Pathway-specific asymmetries between ON and OFF visual signals. J. Neurosci. 38, 9728–9740 (2018).
Chichilnisky, E. J. A simple white noise analysis of neuronal light responses. Network 12, 199–213 (2001).
Yu, W. Q., Grzywacz, N. M., Lee, E. J. & Field, G. D. Cell type-specific changes in retinal ganglion cell function induced by rod death and cone reorganization in rats. J. Neurophysiol. 118, 434–454 (2017).
Anishchenko, A. et al. Receptive field mosaics of retinal ganglion cells are established without visual experience. J. Neurophysiol. 103, 1856–1864 (2010).
Gauthier, J. L. et al. Uniform signal redundancy of parasol and midget ganglion cells in primate retina. J. Neurosci. 29, 4675–4680 (2009).
Watanabe, M. & Rodieck, R. W. Parasol and midget ganglion cells of the primate retina. J. Comp. Neurol. 289, 434–454 (1989).
Angueyra, J. M. & Rieke, F. Origin and effect of phototransduction noise in primate cone photoreceptors. Nat. Neurosci. 16, 1692–1700 (2013).
Donner, K. Noise and the absolute thresholds of cone and rod vision. Vision Res. 32, 853–866 (1992).
Dunn, F. A. & Rieke, F. The impact of photoreceptor noise on retinal gain controls. Curr. Opin. Neurobiol. 16, 363–370 (2006).
Rao-Mirotznik, R., Buchsbaum, G. & Sterling, P. Transmitter concentration at a three-dimensional synapse. J. Neurophysiol. 80, 3163–3172 (1998).
Berry, M. J., Warland, D. K. & Meister, M. The structure and precision of retinal spike trains. Proc. Natl Acad. Sci. USA 94, 5411–5416 (1997).
Freed, M. A. & Liang, Z. Synaptic noise is an information bottleneck in the inner retina during dynamic visual stimulation. J. Physiol. (Lond.) 592, 635–651 (2014).
Atick, J. J. & Redlich, A. N. What does the retina know about natural scenes? Neural Comput. 4, 196–210 (1992).
Brinkman, B. A., Weber, A. I., Rieke, F. & Shea-Brown, E. How do efficient coding strategies depend on origins of noise in neural circuits? PLoS Comput. Biol. 12, e1005150 (2016).
Field, G. D. & Sampath, A. P. Behavioural and physiological limits to vision in mammals. Phil. Trans. R. Soc. Lond. B 372, 20160072 (2017).
Barlow, H. B., Fitzhugh, R. & Kuffler, S. W. Change of organization in the receptive fields of the cat’s retina during dark adaptation. J. Physiol. (Lond.) 137, 338–354 (1957).
Hosoya, T., Baccus, S. A. & Meister, M. Dynamic predictive coding by the retina. Nature 436, 71–77 (2005).
Ringach, D. L. On the origin of the functional architecture of the cortex. PLoS ONE 2, e251 (2007).
Chichilnisky, E. J. & Kalmar, R. S. Functional asymmetries in ON and OFF ganglion cells of primate retina. J. Neurosci. 22, 2737–2747 (2002).
Field, G. D. et al. Spatial properties and functional organization of small bistratified ganglion cells in primate retina. J. Neurosci. 27, 13261–13272 (2007).
Litke, A. et al. What does the eye tell the brain?: Development of a system for the large-scale recording of retinal output activity. IEEE Trans. Nucl. Sci. 51, 1434–1440 (2004).
Lee, J. H. et al. in Advances in Neural Information Processing Systems (eds. Guyon, I. et al.) 4002–4012 (Curran Associates, 2017).
Lee, J. et al. YASS: yet another spike sorter applied to large-scale multi-electrode array recordings in primate retina. Preprint at bioRxiv https://doi.org/10.1101/2020.03.18.997924 (2020).
Shlens, J. et al. The structure of multi-neuron firing patterns in primate retina. J. Neurosci. 26, 8254–8266 (2006).
Gauthier, J. L. et al. Receptive fields in primate retina are coordinated to sample visual space more uniformly. PLoS Biol. 7, e1000063 (2009).
Yao, X. et al. Gap junctions contribute to differential light adaptation across direction-selective retinal ganglion cells. Neuron 100, 216–228.e6 (2018).
Eglen, S. J. The role of retinal waves and synaptic normalization in retinogeniculate development. Phil. Trans. R. Soc. Lond. B 354, 497–506 (1999).
Doi, E., Inui, T., Lee, T. W., Wachtler, T. & Sejnowski, T. J. Spatiochromatic receptive field properties derived from information-theoretic analyses of cone mosaic responses to natural scenes. Neural Comput. 15, 397–417 (2003).
Nocedal, J. & Wright, S. Numerical Optimization (Springer, 2006).
Acknowledgements
We thank L. Glickfeld, S. Lisberger, F. Rieke, J. Kay and F. Wang for comments on drafts of this manuscript, E. J. Chichilnisky and E. Wu for discussions, E. J. Chichilnisky for primate data, and K. Ruda for assistance with experiments. This work was supported by the Ruth K. Broad Postdoctoral Fellowship (S.R.), the Whitehead Scholars Program (G.D.F.) and NIH/NEI R01 EY031396 (G.D.F.).
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This study was conceived by S.R. and G.D.F. S.R. and E.L.D. analysed data. The efficient coding model and optimizations were implemented by N.Y.J. and J.P. The paper was written by S.R. and G.D.F. and edited by all authors.
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Extended data figures and tables
Extended Data Fig. 1 Anti-alignment predicted by efficient coding theory is conserved in mosaics with different densities and boundary conditions.
a, Optimal spatial filters of 48 ON units and 52 OFF units, each on an 18 × 18-pixel grid (orange box). b, The COMs of optimal filters forming the ON (green) and OFF (magenta) mosaics. Training was performed using a circular mask over the images to reduce edge artefacts. c, d, The 2D z-scored IMCE map (c) and radial average z-scored IMCE (d) for the mosaic pairs shown in b. e–h, As in a–d with equal cell density (n = 50) for ON and OFF mosaics. i–l, As in a–d with the number of ON and OFF units fixed at n = 45 and n = 55, respectively. m–p, As in a–d with n = 49 ON units and n = 51 OFF units, but training was performed without a circular mask. Shaded areas, s.d.
Extended Data Fig. 2 Mosaic coordination can persist under widely diverging RF densities.
a–c, Bivariate point pattern (type 1: green, type 2: magenta) generated by modified PIPP model (see Methods) with interaction terms for anti-alignment (a), alignment (b) and independence (c). The density of type 2 points is four times higher than the density of type 1 points. d–f, The 2D z-scored IMCE maps corresponding to a–c, respectively. g–i, The radial average z-scored IMCE averaged over n = 100 mosaic pairs that are aligned (g), anti-aligned (h) and independent (i). Shaded areas are s.e.m.
Extended Data Fig. 3 Mosaic coordination estimates are robust to RF subsampling.
a, RF mosaics illustrating three different cases. Measured, no RFs are removed or added; depleted, a fraction of randomly selected RFs are removed (dashed ellipses); filled, RFs are artificially added to fill mosaic gaps (thick solid ellipses). The gradient below illustrates the percentage of RFs remaining after removing or adding RFs. b, c, Radial average z-scored IMCE for different amounts of subsampling and filling of ON and OFF brisk transient (bt, rat) mosaics (b; blue), ON and OFF brisk sustained (bs, rat) mosaics (b; purple), and ON and OFF parasol (primate) mosaics (c; green). Each curve corresponds to an individual mosaic pair. Results are representative of n = 5 retinas for ON–OFF brisk transient, n = 3 retinas for ON–OFF brisk sustaind, and n = 3 retinas for ON–OFF parasol RGCs. The percentage of RFs relative to measured (100%), is indicated by f. Shaded areas, s.d.
Extended Data Fig. 4 Mosaics encoding distinct visual features appear to be independent.
a, Example mosaics of ON and OFF brisk transient (bt) and brisk sustained (bs) RGC types. Coordination was tested across cell type (orange), and across cell type and polarity (green). b, d, f, h, 2D z-scored IMCE maps of a representative pair (left) and radial average z-scored IMCEs of all pairs (right), for ONbt–ONbs (b, n = 3), OFFbt–OFFbs (d, n = 3), ONbt–OFFbs (f, n = 3), ONbs–OFFbt (h, n = 3) mosaic combinations. Dashed curve, radial average z-scored IMCE corresponding to the 2D z-scored IMCE map (left). Shaded areas, s.d. c, e, g, i, Sampling distributions from bootstrap estimates of mean coordination index for pseudo pairs (grey) and real pairs (orange/green filled circles, arrows). Number of pseudo pairs: n = 12 (c, e, g, i). The grey shaded region to the right of the vertical dashed line indicates value exceeding 95% confidence interval based on one-sample two-sided t-test statistic: P = 0.33, 0.98, 0.37 and 0.46, respectively, for c, e, g and i (n.s., not significant). Cohen’s d = 0.36, −0.006, 0.28 and −0.25, respectively, for c, e, g and i.
Extended Data Fig. 5 Anti-alignment between ON brisk transient RF mosaics persists across light levels.
a, RF mosaics of ON (left) and OFF (right) brisk transient RGCs, measured at photopic light level (10,000 photo-isomerizations per M-cone per s). The COMs of RFs are indicated by black filled circles. b, c, 2D z-scored IMCE map (b) and radial average z-scored IMCE (c) for the mosaic pair shown in a. d, RF mosaics of ON (left) and OFF (right) brisk transient RGC types, at scotopic light level (1.0 photo-isomerizations per rod per s), from the same retina as in a. e, f, As in b, c for the mosaic pairs shown in d. g, Change in RF COMs of ON brisk transient RGCs from photopic to scotopic light level (black filled circles). Solid and dashed red lines show homotypic nearest-neighbour (NN) distances between RFs estimated at photopic and scotopic light levels, respectively. h, Distribution of fractional change in RF position of ON brisk transient RGCs across light levels expressed as a fraction of the mean NN homotypic distance at photopic light level. Smooth curve, kernel density estimate. i, j, As in g, h for OFF brisk transient RGCs. Results are representative of n = 1 retina. Shaded areas, s.d.
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Roy, S., Jun, N.Y., Davis, E.L. et al. Inter-mosaic coordination of retinal receptive fields. Nature 592, 409–413 (2021). https://doi.org/10.1038/s41586-021-03317-5
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DOI: https://doi.org/10.1038/s41586-021-03317-5
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