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Inter-mosaic coordination of retinal receptive fields


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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Fig. 1: Efficient coding predicts anti-alignment between ON and OFF RGCs with similar feature selectivity.
Fig. 2: Analysis framework for measuring mosaic coordination.
Fig. 3: Receptive field mosaics of functionally paired ON and OFF RGC types are anti-aligned.
Fig. 4: Mosaic anti-alignment is unlikely to have arisen by chance.

Data availability

Raw data will be made available upon request. Source data are provided with this paper.

Code availability

Analysis code is available at


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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.).

Author information




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.

Corresponding author

Correspondence to Greg D. Field.

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The authors declare no competing interests.

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Peer review information Nature thanks Daniel Kerschensteiner and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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. eh, As in ad with equal cell density (n = 50) for ON and OFF mosaics. il, As in ad with the number of ON and OFF units fixed at n = 45 and n = 55, respectively. mp, As in ad 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.

ac, 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. df, The 2D z-scored IMCE maps corresponding to ac, respectively. gi, 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.

Extended Data Table 1 The distribution of inter-mosaic coordination energy (IMCE) values is approximately normal
Extended Data Table 2 Coordination index values for real and pseudo mosaic pairs

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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).

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