Mapping a Neural Circuit: A Complete Input-Output Diagram in the Primate

Greg D. Field1*, Jeffrey L. Gauthier1*, Alexander Sher2*, Martin Greschner1, Timothy Machado1, Lauren H. Jepson1, Jonathon Shlens1, Deborah E. Gunning3, Keith Mathieson3, Wladyslaw Dabrowski4, Liam Paninski5, Alan M. Litke2, and E.J. Chichilnisky1

1 Systems Neurobiology Laboratory, Salk Institute for Biological Studies, La Jolla, CA 2 Santa Cruz Institute for Particle Physics, University of California, Santa Cruz, CA 3 Department of Physics and Astronomy, University of Glasgow, Glasgow, UK 4 Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, 23 30-059, Krakow, Poland 5 Department of Statistics and Center for Theoretical Neuroscience, Columbia University, New York, NY * These authors contributed equally.

To understand a neural circuit requires knowing the pattern of connectivity between its inputs and outputs. For example, the role of the retina in color vision depends on the pattern of connectivity between the lattice of (L)ong, (M)iddle and (S)hort-wavelength sensitive cones and multiple types of retinal ganglion cells, each of which samples the visual field uniformly. In the vertebrate nervous system, this kind of comprehensive circuit information has generally been out of reach. Here we report the first measurements detailing functional connectivity between the input and output layers of the primate retina, and we use this information to probe the neural circuitry for color vision. We employed a unique multi-electrode technology to record simultaneously from complete populations of the ganglion cell types that mediate high-resolution vision in primates (midget, parasol, small bistratified). We then used fine-grained visual stimulation to separately identify the location and spectral type of each cone photoreceptor providing input to each ganglion cell. The populations of ON and OFF midget and parasol cells each sampled essentially the complete population of L and M cones. However, only OFF midget cells frequently received at least one strong functional input from an S cone. Statistical analysis revealed a non-random tendency toward pure sampling of either L or M cones in the receptive field centers of midget cells, while inputs to the receptive field surround were apparently random. This purity could not be explained by clumping in the cone mosaic, implying that developmental or adaptive mechanisms enhance red-green color signals sent to the brain.

Color vision requires neural circuitry to compare signals from spectrally distinct cone types. For example, the signature of primate color vision – red-green and blue-yellow color opponency – implies that neural circuits pit signals from different cone types against one another. However, the pattern of connectivity between the three cone types and various (RGC) types, which determines how color signals are 1 transmitted in parallel pathways to the brain, remains incompletely understood 1-9. To probe the circuitry for color vision more fully, we measured the pattern of connectivity between the full lattice of cone photoreceptors and complete populations of RGCs of several types in primate retina.

We recorded from hundreds of RGCs simultaneously in the peripheral macaque monkey retina using a unique large-scale electrophysiological recording system 10,11. The light response properties of each cell were identified by computing the spike- triggered average (STA) stimulus obtained during presentation of spatio-temporal white noise (see Supplementary Methods). From the STA, several features of the light response were identified, including the spatial receptive field (RF) and the time course of the light response. Clustering of all recorded cells based on these properties was used to identify functionally distinct RGC classes (Fig. 1a, center). The RFs of each cell class formed a regular mosaic uniformly covering the region of retina recorded 11,12. This mosaic organization indicated that each functionally defined cell class corresponded to a single RGC type, because each RGC type uniformly tiles the retinal surface with its dendritic arbors 13. The density of cells in each mosaic was used to identify the ON and OFF midget, ON and OFF parasol, and small bistratified cell types, which collectively account for ~60-70% of RGCs 14. In many cases, the RF mosaics exhibited few or no gaps over a substantial region, indicating that essentially every cell of these types had been recorded.

However, traditional RF maps such as these obscure the fact that each RF is composed of the inputs of discrete photoreceptors. To resolve them, RFs were mapped again using white noise stimuli roughly 10-fold finer (pixels 5x5 µm on a side). Measured at this spatial scale, RFs did not conform to the smooth Gaussian approximation used in Fig. 1a (center) and in many previous studies 14. Instead, each RF was composed of multiple punctate islands of light sensitivity, separated by regions of no light sensitivity (Fig. 1a, lower images). The separation was roughly equal to the spacing of cone photoreceptors in the recorded region of retina, consistent with the idea that each island reflected the contribution of a single cone. To test this hypothesis, the locations of the islands were compared to the locations of cone outer segments labeled with peanut agglutinin after the recording; a close alignment was observed (Fig. 1b, see Supplementary Methods).

The spectral type of each cone -- (L)ong, (M)iddle, or (S)hort wavelength sensitive -- was identified using the relative magnitudes of the three display primaries in the STA at its spatial location (Fig. 2a). !These values, accumulated across all cones identified in a single recording, formed three distinct clusters (Fig. 2b). !The clusters were closely aligned with predictions based on the spectral sensitivity of the macaque L, M and S cones. !S cones were easily identifiable, L and M cones were somewhat less so because of their overlapping spectral sensitivities (Fig. 2b,c).

The full cone mosaic was visualized by pooling cone locations and types across all recorded RGCs (Fig. 2d-e). !This was accomplished by fitting the entire collection of cones to the RF data from all RGCs, simultaneously, using a model in which each RF is a sum of Gaussian functions of fixed size, each centered on the location of a cone (see Supplementary Methods). This fit permitted representation of all identified cones in a

2 single diagram, revealing locally nearly complete cone mosaics (Fig. 2d), and mosaics of varying completeness over larger areas (Fig. 2e). !The relative frequencies of L, M and S cones were in an approximate ratio of 8:4:1 (average) in regions with nearly complete cone mosaics, consistent with previous measurements 14,15.

The functional connectivity between each RGC and the cones within its RF was summarized by assigning a weight to each cone, representing the strength of its input. ! The weights were obtained from the fitted model described above. !This approach permitted a well-constrained estimation of the input strength of weak cones, including those in the RF surround (Fig. 2g), because cone locations were robustly identified using data from multiple cells. !The cone inputs to each RGC were summarized using a collection of radiating lines connecting to the cones, with the thickness of each line proportional to the weight, and its shade representing the sign of the input (Fig. 2h). ! This representation permitted simultaneous visualization of a complete mosaic of RGCs and the complete mosaic of the cones they sampled (Fig. 3), i.e. a full functional wiring diagram for the retinal circuits mediating high resolution vision. !A total of 1,961 RGCs connecting to a total of 17,380 cones in 7 preparations were examined.

The complete connectivity diagrams provide a powerful new tool for examining specificity of L, M and S cone inputs to different types of RGCs. This specificity has been a source of controversy, in part because previous studies inferred cone inputs indirectly by manipulating the spectral composition of visual stimuli 1-8 (see Supplementary Discussion). The high resolution connectivity maps (Fig. 3) reveal individual L, M and S cone inputs to each RGC resolved on the basis of their spatial location, solving two major open problems about color circuitry in the retina.

Previous studies provide conflicting accounts of S cone inputs to midget and parasol RGCs 1,4,6,16 (see Supplementary Discussion). In the present data OFF midget cells frequently received at least one strong functional input from an S cone, whereas ON midget, ON parasol and OFF parasol cells did so much less frequently (e.g. see Fig. 3). At the same time, all four RGC types sampled essentially the entire mosaic of L and M cones. A focused example is given in Fig. 4a-c, which shows the connectivity diagram for an ON midget cell and two OFF midget cells sampling the same region; the S cones were sampled by the OFF midget cells but not the ON midget cell. On average, S cones were strongly sampled by OFF midget cells about five-fold more frequently than by ON midget and parasol cells (Fig. 4d; see Supplementary Methods). Additional analysis showed that ON midget cells displayed a tendency to sample weakly from S cones (see Supplementary Methods). The sampling of S cones by OFF midget cells confirms a prediction from anatomical work 16: OFF midget bipolar cells contact S cones in the central primate retina, therefore, OFF midget cells should receive S cone input. The absence of S cone input to parasol cells also confirms recent findings 6. An important question for future work is whether the S cone signals carried by OFF midget cells contribute to blue-yellow and red-green opponent color vision.

The specificity of L and M cone inputs to peripheral midget cells, which is thought to underlie red-green opponent color vision, has been debated extensively (see Supplementary Discussion). One study suggested that midget cells tend to selectively sample from either L or M cones in the RF center, producing red-green color opponency

3 by pitting relatively pure L or M cone center signal against a mixture of L and M cone signals from the surround 2. Another study suggested that the RF surround may sample predominantly from the cone type less strongly sampled by the center, enhancing opponency 7.! Yet another study found no evidence for color opponency in peripheral midget RGCs 15, suggesting that cone sampling is random in both RF center and surround.

In the present data, red-green color opponency was evident in a significant fraction of peripheral midget cells (Fig. 4e).! Color opponency was quantified by calculating the relative strengths of the net inputs from the L, M and S cones over the entire RF, obtained with cone-isolating stimuli (see Supplementary Methods). To examine separately the roles of the RF center and surround in producing opponency, cones were defined as contributing primarily to the RF center or surround based on the sign of their input and their location (see Supplementary Methods). Interestingly, opponency was often strong in those midget cells that sampled either L or M cones dominantly or exclusively in the RF center, while in the RF surround cone sampling seemed indiscriminate (e.g. Fig. 4f-h). These observations are qualitatively consistent with the hypothesis that sampling bias toward either L or M cones in the RF center mediates opponency.! However, across this population of 263 midget cells the purity of cone input to the RF center varied widely (e.g. see Fig. 3c-d), raising the possibility of random sampling in both center and surround.

To test the randomness of L/M cone sampling quantitatively, a statistical analysis was performed, beginning with cones in RF center. First, an index of purity of the cones feeding the RF center was computed for all midget cells in each preparation (Fig. 4i, see Supplementary Methods). The width of the distribution of the purity index quantifies the diversity of cone sampling in the region of retina recorded (Fig. 4j, upper histograms). The purity index was then re-computed after artificially and randomly permuting the identities of L and M cones (Fig. 4j, lower histograms), while preserving all other aspects of the data.! If connectivity between L/M cones and the RF centers of midget cells were random, then permutation of cone identities would not change the distribution of purity index values. In fact, the distribution was significantly narrower after permutation.! For example, fewer cells with pure L or M cone centers (index values near 1 or -1) were observed after permutation.! Permutation reduced purity in nearly all of the populations of ON and OFF midget cells examined (Fig. 4k). Thus, the RF centers of midget cells tend to favor inputs from either L or M cones, contributing to red-green opponency.! In contrast, the same analysis applied to cones in the RF surround had little effect on the purity index (Fig. 4l). This finding is consistent with the hypothesis of random sampling of L and M cone inputs in the surround 15 (see Supplementary Methods).

In principle, the observed sampling bias toward either L or M cones could be produced by clumping in the cone mosaic, that is, a tendency for cones to aggregate with other cones of the same type (Fig. 4m). Such clumping would increase the proportion of midget cells with centers dominated by a single cone type.! Evidence for a weak cone clumping has been reported in central human retina and peripheral macaque retina 17,18, but the implications for color opponent responses in midget cells have not been examined experimentally. Tests for cone clumping on the scale of midget cell RFs in the present data suggested a weak tendency toward clumping, in 3 of 7 cone mosaics

4 analyzed (see Supplementary Methods). However, the weak clumping observed could not account for the observed purity.! This was determined by generating artificial cone mosaics with the same degree of clumping as the measured cone mosaic (see Supplementary Methods), and observing that the purity of midget cells in the raw data was substantially larger than with artificially clumped mosaics (Fig. 4m).! Thus cone type purity in midget cell RFs cannot be explained by cone clumping, implying that midget cells must sample L and M cone inputs, through the retinal network, in a selective manner. ! This selective sampling could be produced if (1) each midget cell receives inputs from one cone type more frequently than the other (Fig. 4n), and/or (2) each midget cell weighs inputs from one cone type more strongly than the other (Fig. 4o). Statistical analysis suggested that both mechanisms contribute to purity. In model (1), the number of cones sampled by each midget cell should be skewed toward one cone type or the other. Therefore, random permutation of L/M cone identities should reduce purity, even if the relative weights of different cone inputs to each cell are ignored.! This prediction was confirmed (Fig. 4n). In model (2), the weights on cones in each midget cell should be skewed toward one cone type or another. Therefore, random permutation of the strength of all the cone inputs within the RF of each midget cell should reduce purity.! This prediction was also confirmed (Fig. 4o), though the effect was modest.! Control analysis indicated that these statistical findings were not a simple result of the tapering RF profile of RGCs, or the small apparent clumping in the cone mosaic (data not shown).

Selective sampling has implications for the mechanisms by which retinal circuitry is coordinated. The divergence of the L and M cone photopigments in primates is relatively recent 19, and there is little evidence for segregation of L and M cone signals in the retinal circuitry 20. L and M cones are apparently indistinguishable both anatomically and histochemically and the opsins exhibit 96% mutual identity 21. Furthermore, there is only tentative anatomical evidence of differences in pathways conveying L and M cone signals downstream 22, in contrast to the strikingly different pathway that conveys S cone signals 23,24. Therefore, a structural or molecular basis for the observed selectivity seems unlikely.

Given this backdrop, it is tempting to speculate that selective sampling could arise from activity dependent adjustment of synaptic inputs. !At the eccentricites recorded, midget bipolar cells usually contact only one cone 25, providing an opportunity for midget RGCs to selectively sample inputs from bipolar cells carrying signals from one cone type or the other. These bipolar cells could in principle be distinguished by the statistics of their responses to natural scenes 26. The possibility of an adaptive mechanism to achieve selective sampling is broadly consistent with recent observations of long-term adaptability in retinal signals (see 27) and color vision 28.

The circuitry of color vision is just one aspect of sensory processing that may be fruitfully explored using cell-by-cell functional circuit mapping. For example, in the , measuring the full transformation between sensory layers could help clarify important neural computations such as adaptation to spatial contrast, direction selectivity, and object motion sensitivity (see 27).

5 Contact: E.J. Chichilnisky, Systems Neurobiology, The Salk Institute, 10010 North Torrey Pines Road, La Jolla, CA 92037, USA. email: [email protected], phone: (858) 453-4100 x1286.

Acknowledgements: This work was supported by the Helen Hay Whitney Foundation (G.D.F.), DFG (M.G.), NIH NRSA (NS054519-01) and Chapman Foundation (J.L.G.), Miller Institute for Basic Research in Science, University of CA, Berkeley (J.S.), Polish Ministry of Science and Higher Education (W.D.), Burroughs Wellcome Fund Career Award at Scientific Interface (A.S.), McKnight Foundation (A.M.L. & E.J.C.), NSF Grant PHY-0750525 (A.M.L.), a Sloan Research Fellowship, and NIH Grant EY13150 (E.J.C). We thank C.K. Hulse for technical assistance; M.I. Grivich, D. Petrusca, A. Grillo, P. Grybos, P. Hottowy, and S. Kachiguine for technical development; H. Fox, M. Taffe, E. Callaway and K. Osborn for providing access to ; S. Barry for machining; F. Rieke and T. Sejnowski for providing comments on the manuscript. We thank the San Diego Supercomputer Center and the NSF (Cooperative Agreements 05253071 and 0438741) for large scale data storage.

Author Contributions: G.D.F., J.L.G., A.S., and E.J.C. conceived the experiments. G.D.F., J.L.G., A.S., M.G., J.S., and E.J.C. performed the electrophysiological experiments. G.D.F, J.L.G., A.S., M.G., T.A.M., and L.P., analyzed the data. A.S., D.E.G., K.M., W.D., A.M.L. provided and supported the large-scale multielectrode array system. G.D.F. and E.J.C. wrote the manuscript.

6 Figure Legends

Figure 1: Cell type classification and single cone receptive field (RF) maps. (a) Cell type identification using the spike-triggered average (STA) of white noise stimuli (see Supplementary Methods), for 323 cells recorded simultaneously from a single macaque monkey retina. Central scatter plot shows RF radius (1 SD of Gaussian fit to spatial profile of STA) and the time course of the STA (projection onto the first principal component), for all cells recorded. Surrounding panels show Gaussian fits to the RFs of the cells from each distinct cluster in the scatter plot; the fits are represented as ellipses (1 SD boundary of fit). Hexagons indicate outlines of the electrode array. The density and light response properties of cells in each group were used to identify them as the ON and OFF midget, ON and OFF parasol, and small bistratified types 29. Outermost panels show sample spatial RF and Gaussian fit for a representative cell of each type (ellipses for sample cells are darkened in the central panels). Each scale bar is 60 "m. The punctate islands of light sensitivity in these RFs, separated by regions of no light sensitivity, appear to represent the contribution of individual cones. (b) Confirmation of cone photoreceptor inputs in RF maps. First and second panels show spatial RF profiles of a single ON midget and a single ON exhibiting punctate islands of light sensitivity. Putative locations of cones in the RFs identified by thresholding are marked with black dots. Third panel shows the map of putative cones assembled from all cells with RFs covering this region of retina. Fourth panel shows putative cone locations overlaid on a photograph of cone outer segments labeled with fluorescently tagged peanut agglutinin (see Supplementary Methods).

Figure 2. Identification of cone mosaics and strength of inputs to RGCs. (a) Images show spatial RFs of one ON midget and one OFF midget cell from a single recording. For each cell, the spectral sensitivity of 4 individual cones is summarized in flanking pie charts showing the relative magnitude of the red, green and blue display primaries in the STA, expressed as differences from the mean. A distinguishing feature of putative L and M cones (left vs. right pies) is the relative magnitude of the blue and red primaries. (b) For all cones identified in a single recording, the relative magnitudes of the display primaries are shown as points on the surface of a sphere in the three- dimensional space. Colored lines show the expected locations of the L, M and S cones obtained using the spectral sensitivity of the three cone types and the calibrated spectral emission of the display. Each point is colored according to its assigned identity as L (red), M (green), or S (blue). (c) Classification of L and M cones is quantified with a histogram of points from (b), projected on to the line joining the predicted locations of the L and M cones. Bars are colored according to the cone classification; S cones are omitted. (d) Assembled estimated cone mosaic over a local region is shown as a collection of colored dots. The cones identified from the two cells in (a) are highlighted with white circles. Note the regular spacing of cones, suggesting completeness of the estimated cone mosaic over this region of retina. (e) Entire cone mosaic from a single recording (2,373 cones). (f-h) Illustration of strength of input from center and surround to a single OFF midget cell. (f) The raw STA is shown with overlaid local cone mosaic. The strength of the input from each cone is reflected in the contrast of the STA at the pixel locations under the cone. (g) The raw STA is shown with positive values truncated 7 and remaining contrast values renormalized, emphasizing the weaker opposite sign weights on cones in the RF surround. (h) Connectivity diagram illustrating the strength of each cone input to the cell. The thickness of each line is proportional to the input strength derived from the STA. Center and surround cones are shown with white and black lines respectively. Surround cone line thicknesses were increased five-fold relative to center cone line thicknesses for visibility.

Figure 3. Full sampling of cone photoreceptor lattice by multiple RGC types. Each panel shows a mosaic of cones identified in a single recording represented as colored dots, with the connectivity diagrams for all RGCs of a single type over that region. The cone mosaic is identical in all four panels. For simplicity, connectivity diagrams only reflect the RF center (see Supplementary Methods). Cones feeding the RF center of at least one RGC are highlighted with a white annulus around the colored circle. In this region, at least 14 significant connections were observed between OFF midget cells and the 24 S cones identified in the region. Yet, among ON midget, ON parasol and OFF parasol cells, only 1, 0, and 0 connections to S cones were observed, respectively. Scale bar: 50 µm.

Figure 4. Specificity of cone inputs to midget and parasol cells. (a-c) Connectivity diagrams reveal no S cone inputs to an ON midget cell (a) despite nearby S cones within its RF (arrows) that provide inputs to nearby OFF midget cells (b,c). (d) Frequency of strong S cone sampling by ON and OFF midget and parasol cells (see Supplementary Methods). (e) Normalized cone inputs to ON and OFF midget cells in a single preparation. Each point shows the normalized L, M and S cone input strength to a single midget cell, summed over the entire RF, measured with a cone-isolating coarse white noise stimulus (see Supplementary Methods). Points in the upper right and lower left quadrants represent cells for which the net input of both L and M cones was ON and OFF, respectively (non-opponent). Points in the other quadrants represent cells for which the net L and M cone inputs had opposite sign (opponent). Points on the diagonals indicate cells with no S cone input, points inside indicate S cone input. (f-h) Connectivity diagrams for three midget cells, the first two (f,g) illustrating relatively pure input from L or M cones to the RF center, the third (h) showing mixed L and M cone input. Summed cone inputs for these cells are indicated with corresponding letters in (e). (i) Schematic of cone type purity index (see Supplementary Methods). (j) (Top) Distributions of cone type purity index for ON and OFF midget cells in a single preparation. (Bottom) Distributions of the purity index computed with a cone mosaic in which L and M cone identities have been randomly permuted. These distributions have SDs in the range of 0.37±0.04 and 0.36±0.04 (mean ± 2 SD), significantly lower than the values of 0.45 and 0.44 obtained from the data. (k) Comparison of purity index obtained with real and permuted cone mosaics. Each point represents the width (SD) of the purity index distribution from a collection of at least 50 simultaneously recorded ON or OFF midget cells. Error bar indicates 1 SD of the width across 64 random permutations of cone types. Points below the diagonal indicate greater purity in the data than with permuted cones. (l) Same analysis as (k), but applied to cones from the RF surround. (m) (Left) Schematic of cone clumping increasing purity. (Right) Analysis of cone clumping. Same as k, but using random cone mosaics with the same degree of

8 clumping as the data (see Supplementary Methods). (n) (Left) Schematic of biased sampling increasing purity. M cone dominated cell avoids nearby L cones and contacts more distant M cones. (Right) Analysis of biased sampling. Same as (k), but with cone weights in Equation 1 binarized to either 0 or 1 before computing purity. (o) (Left) Schematic of biased weighting increasing purity. M cone dominated cell samples L cones weakly (thin lines) and M cones strongly (thick lines). (Right) Analysis of biased weighting. Same as (k), but with random permutation of the weights on the cones in the RF center, rather than cone types.

9 Methods

General

Most of the methods are described in Supplementary Methods. Elecrophysiological procedures, spike identification, stimulus generation and calibration, receptive field characterization, and cell type classification were performed largely using previously described methods 29. Imaging of cone outer segments was performed using standard methods. New methods were developed for cone identification and classification. Here, details are given on analysis methods for testing cone type purity in RGC receptive fields.

Analysis of cone type purity

The degree of purity of L and M cone input to RGCs was quantified using an index:

" Li ! " M j i j (1) " Li + " M j i j where Li and Mj represent the weights on distinct L and M cones in the RF. Thus, if all cones sampled were L (M) cones, the index would be 1 (-1) (Fig. 4i). If the weighted input were equal for L and M cones, the index would be zero. This index was computed separately for cones in the RF center and surround.

To examine purity in populations, the distribution of purity indices was generated for all ON midget cells!and all OFF midget cells (Fig. 4j). The width (SD) of this distribution was compared to that of a null distribution, which was generated by artificially and randomly permuting cone types in the cone mosaic, recomputing purity indices for all RGCs, and then determining the SD of this distribution. This value represents the expectation if cone types are randomly spatially distributed and randomly sampled by RGCs. To statistically compare the permutation to the data (e.g. Fig. 4k error bars), cone mosaics were re-permuted 64 times and the SD across permutations was obtained.

Several control analyses were performed to verify the finding that midget cells exhibited non-random cone purity (Fig. 4k). First, the analysis was run using a more stringent criterion, and a more permissive criterion, for the identification of cones in the data set, by altering the stopping point used in the automated cone identification algorithm. Second, the analysis was run for each cell type (e.g. ON midget) using cones identified only from the RFs of other cone types (e.g. OFF midget, ON parasol, OFF parasol, small bistratified). Third, analysis was performed using an entirely different procedure to identify cones (Supplementary Methods). These analyses produced results essentially indistinguishable from the original finding.

10 Analysis of cone clumping and effects on purity

To test whether mosaics of L and M cones exhibited clumping, an index was calculated that summarized the degree of aggregation of each cone type on the spatial scale of the midget cell RF:

" 1 2 % c exp (D / r) (2) = ) $! ij ' i( j # 2 & where Dij is the distance between the ith and jth cone, r is the average RF radius of midget cells, and summation is performed over all cone pairs of the same type (either L or M).! If the cone mosaics in the data were clumped on the spatial scale of the midget cell RF, then randomly permuting L and M cone labels in the data should destroy this clumping and reduce the index. In four data sets examined, the degree of clumping in the data was within 1 SD of the distribution of clumping values obtained with repeated permutations of cone types, while in the remaining three data sets the value was 2-3 SDs of permutations. Similar results were obtained with spatial scales r twice and half as large. Simulations indicated that these results could be explained by systematic errors in L/M cone classification of 2-5%.! Estimated L/M cone classification error rates ranged from 1-6% (mean = 3.4%) across 7 preparations.! Thus, the weak evidence for clumping was consistent with an origin in small cone type classification errors.

Three additional statistical tests of clumping were performed as controls.! These have the advantage of testing multiple spatial scales.! The three tests compared cumulative distributions of three distance measurements from an observed mosaic of L and M cones to values computed from the same mosaic after cone type permutation.! The three tests were based on the distribution of inter-cone distances 17, nearest neighbor distances, and distances from cones to an artificial square lattice of points (statistics H, G, and F respectively from 30). For these three tests respectively, 1/7, 3/7, and 2/7 of cone mosaics examined exhibited evidence for clumping of either L or M cones at p < 0.01 at some spatial scale. There was no spatial scale that consistently yielded indications of clumping, and only 1/7 data sets suggested clumping in all three tests. Thus, these tests also provided at most weak evidence for clumping of L or M cones.

However, even weak clumping could contribute to apparent cone type purity in the RF center. To test this possibility, artificial cone mosaics with a clumping index (5) matching the data were generated by first randomly permuting the cone labels of an observed cone mosaic, then swapping the labels of randomly selected L,M cone pairs if the swap increased the index, iterating until the clumping index matched that of the data. Many such artificially clumped cone mosaics were generated, and the purity of midget cell RFs was compared with real and artificial mosaics (Fig. 4m).

As a control, analysis was performed by shifting the cone mosaic with respect to RGCs instead. This was done by selecting a collection of RGCs, translating the cone lattice with respect to them, and then associating with each RGC the set of cones closest to the locations of the original cones in its original RF. Across many randomly selected shifts of the cone mosaic, this manipulation also reduced purity (Figure 7b), confirming that the observed purity is not explained by purely by clumping in the cone mosaic. 11 Analysis of biased sampling and weighting

Variations of the purity analysis tested the contribution of biased sampling and biased weighting to the purity of midget cell RF centers. To test biased sampling, the same analysis described above was performed, however the weights of cones feeding the RF center of each RGC were first set to one, other weights were set to zero (Fig. 4n). This produced a purity analysis based on the collection of cones feeding the RF center while ignoring the weights on those cones. To test biased weighting, the weights of cone providing input to each RGC were permuted (Fig. 4o). This kept the collection of cones feeding each RGC constant, but eliminated any relationship between cone type and cone weight.

12 References

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14 Figure 1 a time course projection (a.u.) off midget -1 0 1 on midget

400 radius (!m)

off parasol on parasol SBC

b on midget on parasol map of cones alignment Figure 2 a d on midget l cones m cones

off midget

b blue e

red

green c 160

80 counts

0 -0.2 0 0.2 M-L cone axis f g h Figure 3 a on parasol b off parasol

c on midget d off midget Figure 4 a on midget b off midget c off midget d

on parasol

off parasol

on midget

off midget

0 1.0 s cone efficiency

f on midget g off midget h off midget e 1 f L cone

g

0.5 -1 1 M cone

h -1

i j on midgets off midgets k l 0.5 0.5 data surround 30 30 center

0 0 count permuted 40 35 -1.0 0.0 1.0 permuted cones permuted cones

purity index count 0 0 0 0.5 0 0.5 -1.0 0.0 1.0 -1.0 0.0 1.0 data data purity index purity index m n o cone clumping biased sampling biased connctivity 0.5 0.5 0.5 permuted cones 0 0.5 0 0.5 permuted weights 0 0.5

permuted w/ clumping data binarized weights data