Retinal origin of orientation maps in visual cortex

Journal name:
Nature Neuroscience
Year published:
Published online


The orientation map is a hallmark of primary visual cortex in higher mammals. It is not yet known how orientation maps develop, what function they have in visual processing and why some species lack them. Here we advance the notion that quasi-periodic orientation maps are established by moiré interference of regularly spaced ON- and OFF-center retinal ganglion cell mosaics. A key prediction of the theory is that the centers of iso-orientation domains must be arranged in a hexagonal lattice on the cortical surface. Here we show that such a pattern is observed in individuals of four different species: monkeys, cats, tree shrews and ferrets. The proposed mechanism explains how orientation maps can develop without requiring precise patterns of spontaneous activity or molecular guidance. Further, it offers a possible account for the emergence of orientation tuning in single neurons despite the absence of orderly orientation maps in rodents species.

At a glance


  1. Orientation maps as moire interference patterns between retinal ganglion cell mosaics.
    Figure 1: Orientation maps as moiré interference patterns between retinal ganglion cell mosaics.

    (a) The superposition of two hexagonal lattices results in a periodic interference pattern. (b) Locally, patterns are organized into pairs of dipoles, in which cells of opposite center sign are nearest neighbors of each other. Cortical pooling of inputs from a dipole (relayed by the LGN) would result in simple-cell receptive fields with side-by-side ON and OFF subregions. (c) The period of the interference pattern is a function of the ratio between the lattice spacing in the two mosaics and their relative orientation. The operating points a, b and c lead to scaling factors of 21, 8.1 and 2.2, respectively, and these operating regimes are also used in the following figures. (d) Example of an orientation map generated from a moiré interference pattern. The left panel shows the moiré interference pattern between ON- and OFF-center receptive fields. Shaded areas on the moiré interference pattern show that dipoles with the same orientation arrange themselves as vertices of a hexagonal lattice pattern (see also Fig. 2c). In the right panel, which represents the same area shown by the pattern on the left, the resulting cortical orientation tuning is shown in two ways. The left half of the map shows the preferred orientation of well tuned cortical cells (orientation selectivity index >0.25; see Online Methods) coded by their preferred orientation. The smooth map in the right half is obtained by Gaussian filtering of these strongly tuned orientation signals (see Online Methods for details). Dipole orientation (left panel) determines the preferred orientation of the best-tuned neurons in the cortex (right panel). Outlined white circles on the right panel correspond to the same iso-orientation domains depicted on the interference pattern on the left.

  2. Moire scaling factor and orientation map periodicity.
    Figure 2: Moiré scaling factor and orientation map periodicity.

    Each column depicts examples of different scaling factors. The operating regimes illustrated are the ones shown by a, b and c in Figure 1c. (a) Examples of the resulting moiré interference patterns. (b) The preferred orientations of well tuned cells (left) and filtered orientation maps (right). Format as in Figure 1d. (c) Autocorrelations of orientation maps show hexagonal structure, indicating that iso-orientation domains lie on a hexagonal lattice (see also Fig. 1d). (d) Enlarged area from the maps in b showing the predicted micro-architecture of orientation preference. Preferred orientation changes gradually in the left and middle panels. In the right panel, orientations are distributed as a salt-and-pepper-like pattern. (e) Histogram of the orientation differences between pairs of nearby cells (<100 μm) on the cortical surface. Similar orientations cluster in the left and middle panels. In the right panel, preferred orientations at nearby locations are uncorrelated. The uniform distribution of angular differences in the right histogram is a signature of salt-and-pepper organization. Scale bar in a, 1 mm on the retinal surface. Scale bars in bd, 1 mm of cortical space.

  3. Hexagonal structure of orientation maps.
    Figure 3: Hexagonal structure of orientation maps.

    (a) The autocorrelation structure of orientation maps are shown for two different animals in four species. Secondary peaks (solid black circles) in the autocorrelation function form an approximate hexagonal structure in all cases. The magnitudes of all of these local maxima are statistically significant (bootstrap analysis, P < 0.002). The scale bar equals the orientation map period. (b) The average autocorrelation function across all animals shows local peaks (open white squares) that match closely the ones predicted by a perfect hexagonal lattice (open white circles). The solid black circles represent the locations of all the local maxima (shown in panel a) after the normalization step. White contour lines are plotted at a correlation coefficient of 0.33 to illustrate the separation of local peaks. The scale bar equals the orientation map period. (c) Angular location of local peaks in the autocorrelation function in panel b relative to the reference peak. The distribution is bimodal with modes near 60 and 120 degrees, as predicted by the model. Bimodality was established by a mixture of von Mises distributions using the Bayes information criterion to select the order of the model. The red solid line shows the probability distribution of the best fit. (d) The same analysis performed on control maps. Here the distribution of local peaks is much more isotropic. (e) One component (red line) is sufficient to account for the control data. In ad local peaks were considered only if their distances to the origin were within ±33% of the map period.

  4. Robustness of seeded map to positional noise.
    Figure 4: Robustness of seeded map to positional noise.

    (a) The addition of independent Gaussian noise of an appropriate magnitude to the positions of vertices in the hexagonal lattice enables the model RGC mosaic to match the statistics of nearest-neighbor distance distributions observed experimentally, both within and across cell types. The experimental data show the distance between receptive field center locations. The standard deviation of the Gaussian noise required to match these distributions is σ = 0.12d. (b) The periodicity and strength of the seeded structure can be measured by the distance from the origin (black arrows) and magnitude of secondary peaks (white arrow) in the autocorrelation of the orientation map. As noise increases to realistic values, the secondary peak in autocorrelation remains strong and the map period is invariant, showing the robustness of the moiré interference pattern. The map period is plotted normalized to that attained in the absence of positional noise. (c) The percentage of ON–OFF dipoles originally present in the noise-free interference pattern that are lost with increasing noise. The vertical line indicates the level required to match nearest-neighbor distributions, σ = 0.12d. For this value of noise, 27% of the dipoles are lost on average. (d) Dipoles that survive the perturbation of their location will have their original orientation perturbed. The histogram shows the distribution of changes in orientation in a dipole from its original orientation at experimental noise values, σ = 0.12d.

  5. Robustness of receptive field shapes at different operating regimes of the model.
    Figure 5: Robustness of receptive field shapes at different operating regimes of the model.

    Receptive field structure was evaluated by the distribution of (nx,ny) and of spatial phases of the simulated receptive fields. The distributions are similar for the different operating regimes, even though some do not support the existence of smooth orientation maps. Insets show the distributions of spatial phases in broadly tuned (bottom 50%) and sharply tuned (top 10%) simulated receptive fields.


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  1. Department of Neurobiology, David Geffen School of Medicine, University of California, Los Angeles, California, USA.

    • Se-Bum Paik &
    • Dario L Ringach
  2. Department of Psychology, University of California, Los Angeles, California, USA.

    • Dario L Ringach


Both S.-B.P. and D.L.R. were responsible for the theoretical concepts, computer simulations and writing.

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