Target specific routing of visual information by the superior colliculus

The superior colliculus is an important node in the visual system that receives inputs from the retina and distributes these visual features to various downstream brain nuclei. It remains unknown how these circuits are wired to enable specific and reliable information processing. Here the retinal ganglion cells at the beginning of two such circuits, one targeting the pulvinar and the other the parabigeminal nucleus, were labeled using mono-synaptically restricted rabies tracing. Instead of a fuzzy distribution of the retinal outputs, we delineate clear preferences in how information is routed to these two targets. Three retinal ganglion cell types selectively innervated circuits projecting to the pulvinar, six are preferentially routed to the parabigeminal nucleus, and three innervate both circuits. This work argues that neural circuits of the superior colliculus are based on a dedicated set of connections between specific retinal ganglion cell types and different targets of the superior colliculus.


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The nervous system is built from a large set of diverse neuronal cell types that work together to process 22 information and guide behavior 1 . The neuronal circuits underlying these actions can broadly be divided 23 into two categories. 'Hard-wired' circuits that enable robust and stereotyped behavioral responses 2-4 , and 24 flexible networks that modify their computations based on context and experience 5,6 . Many innate 25 behaviors rely on subcortical circuits involving the same well-defined sets of brain structures in different 26 species 7-10 . However, in the visual system it remains unclear to what extent any one brain region has 27 hard-wired rules linking its inputs with its downstream targets [11][12][13][14][15][16] . 28 The output of the retina encodes over 40 features of the visual scene [17][18][19] . Each feature is transmitted by a 29 distinct retinal ganglion cell type, which can be distinguished by its dendritic anatomy, response 30 properties, or molecular and genetic markers [17][18][19][20][21][22] . One of the major retinorecipient areas is the superior 31 colliculus, which receives approximately 90% of the retinal outputs in rodents 16,23-25 . 32 The retinal inputs to the superior colliculus innervate its superficial layers, which consist of several 33 groups of neurons with diverse morphology, visual response properties and mid-brain targets including 34 the lateral pulvinar, lateral geniculate nucleus and parabigeminal nucleus 15,26-30 . Each retino-recipient 35 neuron of the superior colliculus has been estimated to receive input from at least four retinal ganglion 36 cells 31 . Some level of specificity has been demonstrated for direction-selective neurons, which receive 37 input from direction-selective neurons of the retina 32 . However, as projection specific transsynaptic 38 tracing has not been performed it remains unknown what the distribution of ganglion cell types is that 39 synapse onto a group of neurons with a shared projection. This has left unanswered questions about 40 whether each output pathway of the superior colliculus shares a common input logic, and consequently 41 whether the different behaviors initiated by the colliculus are based on different collections of visual 42 features. 43 To determine the wiring rules by which the retinal output is routed by the superior colliculus to different 44 downstream nuclei, we used a combination of monosynaptic viral tracing and molecular markers to 45 specifically label the retinal ganglion cells at the beginning of two circuits targeting the parabigeminal 46 nucleus (colliculo-parabigmeinal circuit) and the pulvinar (colliculo-pulvinar circuit). Using quantitative 47 analysis of the retinal ganglion cell morphology, we found strong preferences for hard-wired rules 48 governing the routing of visual information through the superior colliculus. 49

Transsynaptic tracing of retinal ganglion cells from targets of the superior colliculus 51
To characterize how visual features are routed by the mouse superior colliculus to two distinct brain 52 nuclei, we used viral tools to label the retinal ganglion cells innervating each circuit (Figure 1). This 53 involved injecting either the parabigeminal nucleus ( Figure 1A-D) or lateral pulvinar ( Figure 1E-H) with 54 a herpes-simplex virus that expressed rabies-G, TVA and mCherry ( Figure 1A for parabigeminal nucleus, 55 Figure 1E for pulvinar). In the case of the parabigeminal nucleus, no other target structures of the 56 superficial superior colliculus are in close vicinity 15,26,30 . However, the lateral pulvinar is near the lateral 57 geniculate nucleus, another target of the superior colliculus. To ensure specific infection of neurons 58 projecting to the lateral pulvinar we used the NSTR1-GN209-Cre mouse line that labels neurons 59 projecting uniquely to the lateral pulvinar 15 . Subsequently, we injected an EnvA-coated rabies virus 60 coding for the fluorescent protein GCaMP6s (EnvA-SADΔG-GCaMP6s) into the superficial layers of the 61 superior colliculus. This transsynaptic viral infection strategy allowed us to specifically express the 62 fluorescent marker GCaMP6s in several dozen retinal ganglion cells per retina that send information to 63 the targeted circuit ( Figure 1C and D for parabigeminal nucleus; Figure 1G and H for the pulvinar). 64 To extract the morphology of single labelled ganglion cells, we stained retinas with antibodies against 65 GFP (binding to the GCaMP6s) and ChAT, which labels starburst amacrine cells ( Figure 1I). The 66 dendrites of starburst amacrine cells form two distinct bands in the inner plexiform layer that are 67 commonly used to quantify the dendritic stratification level of retinal ganglion cells 18,33 . We imaged 68 individual ganglion cells with a confocal microscope, creating high-resolution z-stacks of the labelled cell 69 and ChAT-bands. Cells were chosen for analysis if their dendrites showed little overlap with 70 neighbouring cells in the same depth of the inner plexiform layer. Applying a semi-automated routine, we 71 then created a flattened version of the imaged cells 33,34 . 72 The en-face and side-view of the dendrites of 16 example cells are shown in Figure 1J. We extracted the 73 morphology of 146 ganglion cells after injections into the parabigeminal nucleus and 155 cells after 74 lateral pulvinar injections (total: 301 cells from 58 retinas). In this collection, we found a variety of cell 75 morphologies: ~10% of the analyzed cells are bistratified retinal ganglion cells with dendrites at two 76 locations in the inner plexiform layer (n = 31); ~20% are mono-stratified with dendrites below the ChAT-77 bands (n = 60); ~41% are mono-stratified with dendrites between the ChAT-bands (n = 124); and ~29% 78 were OFF-cells with dendrites stratifying above the ChAT-bands (n = 86). To quantify the morphology of 79 each ganglion cell, we created a density profile of each cell's dendrites relative to the ChAT-bands (Fig  80  S1E) and measured the area covered by the dendrites. Our dataset contains cells with dendritic field 81 diameters of 90 to 420 µm (median: 206 µm, Fig S1F), which is similar to the reported range of 80 to 530 82 µm 35-38 . The ganglion cells labelled here thus cover the known range of dendritic stratification and size. 83

Retinal inputs to the parabigeminal and the pulvinar circuit differ in size and stratification 84
In a first step, we compared the set of retinal ganglion cells that provide input to the parabigeminal and 85 the lateral pulvinar circuits ( Figure 2). We found that retinal ganglion cells sending information to the 86 parabigeminal nucleus on average have larger dendritic trees (median: 232 m) than the cells innervating 87 the colliculo-pulvinar circuit (median: 186 m; p < .01, Kolmogorov-Smirnov test; Figure 2A). 88 Additionally, the lateral pulvinar has a strong bias for retinal ganglion cells stratifying between (50.3%) 89 or above (32.9%) the ChAT-bands and has almost no inputs from bistratified neurons (2.6%; Figure 2B). 90 Approximately 14.2% of neurons are below the ChAT-bands. The parabigeminal nucleus, on the other 91 hand, receives inputs from all four groups of ganglion cells (bistratified 18.5%, below 26.0%, between 92 31.5%, above 24.0% ChAT-bands; Figure 2B). We show that ganglion cells of the parabigeminal circuit 93 are generally larger at all dendritic stratification depths (below ChAT-bands: 280 m (parabigeminal) vs 94 183 m (pulvinar); between ChAT-bands: 185 m vs 130 m; above ChAT-bands: 234 m vs 170 m; 95 Figure 2C). In each of these anatomical divisions the size distributions and medians are statistically 96 different (p < .01; Kolmogorov-Smirnov test and Wilcoxon rank sum test). 97 Overview of retinal ganglion cells in the two circuits. I) Side-view of z-stack scans of four example retinal ganglion cells (green) and the ChAT-bands (magenta). Scale bar = 20 µm. J) 16 retinal ganglion cells from either injection approach (parabigeminal nucleus or pulvinar). Top: en-face view of the dendritic tree. Bottom: side-view of the dendritic tree. Location of ChAT-bands is indicated with two orange lines. The cells have been broadly separated into four stratification groups: bistratified (first column), below ChAT-bands (second column), between ChAT-bands (third column), and above ChAT-bands (last column).
To determine if these differences are due to a bias in the retinotopic location of the sampled ganglion cells, 99 we checked the spatial distribution across the retina of the labeled neurons. For each circuit we sampled 100 from all retinal quadrants at various eccentricities ( Figure 2D-F). 33% of labelled ganglion cells were 101 sampled from the central third of the retina (between 0 µm and 833 µm from the optic nerve; 1.5 cells per 102 10 5 µm 2 ), 53% from the middle third (between 833 µm and 1667 µm from the optic nerve; 0.8 cells per 103 10 5 µm 2 ) and 14% from the peripheral third (between 1667 µm and 2500 µm from the optic nerve; 0.1 104 cells per 10 5 µm 2 ). Further, we sampled 25% of all cells from the upper left quadrant (naso-dorsal), 27% 105 from the upper right (dorso-temporal), 21% from the lower right (temporo-ventral) and 27% from the 106 lower left quadrant (ventro-nasal). This indicates that the observed difference in size between the two 107 circuits is not due to a sampling bias in retinotopic location. 108

Retinal inputs to the parabigeminal and the pulvinar circuit differ in molecular signature 110
To identify the types of retinal ganglion cells in our dataset, we performed histological staining against 111 known molecular markers of ganglion cell types. One set of retinal ganglion cells that can be labelled 112 using antibodies are the alpha cells, which in mice form a group of four ganglion cell types that can be 113 distinguished based on their dendritic stratification and labeling using SMI32-antibodies against 114 neurofilament 35,39-42 . This group of neurons contains two ON and two OFF cells that include: a sustained 115 ON-type lying just below the ChAT-bands; a transient ON-and transient OFF-type stratifying between 116 the ChAT-bands and a sustained OFF-type with dendrites above the ChAT-bands 40 . We found that 117 around half of all rabies-labelled cells innervating the parabigeminal (median: 42%, range: 41 to 53%, n = 118 3 retinas; Figure 3A-C), and the pulvinar circuits (median: 53%, range: 45 to 56%, n = 4 retinas; Figure  119 3E-G) are alpha-cells (SMI32 + ). To identify which of the four alpha cell types are part of each circuit, we 120 acquired local z-stacks of 91 SMI32 + /GCaMP6s + double labeled neurons from 3 parabigeminal 121 experiments, and 90 SMI32 + /GCaMP6s + cells from 3 pulvinar experiments. Each neuron was manually 122 grouped into one of the four types based on its dendritic stratification depth ( Figure 3D and 3H Three out of the four types can be labelled with anti-CART antibodies 43 . We performed anti-CART 136 histological staining in a subset of the retinas from both experimental assays ( Figure 4). Double labeled 137 neurons (GCaMP6s and CART) are found almost exclusively only after retrograde tracing from the 138 parabigeminal nucleus (median: 6.9% of all GCaMP6s-postive cells, range: 4.3 to 9.1%, n = 3 retinas). In 139 the pulvinar experiments, a negligible percentage of the labelled ganglion cells are CART + (median: 1.3%, 140 range: 0 to 2.1%, n = 6 retinas). In two of the retinas we saw no double labeled neurons (0/34 and 0/536). 141 To characterize the rules by which circuits of the superior colliculus projecting to the parabigeminal 145 nucleus and the pulvinar sample retinal inputs, we clustered our morphological data taking into 146 consideration information about molecular identity. This allowed us to know the molecular identity of 54 147 out of the 301 ganglion cells in our data set (n = 51 for SMI32; n = 3 for CART). We first set the average 148 dendritic stratification profile for each genetically identified cell type as a cluster centroid (4 SMI32 + 149 types and 1 CART + group). Then, all cells were clustered using an affinity-propagation based algorithm 44 . 150 This resulted in 12 clusters based on three validation indices ( Figure 5A). Figure 5B shows a low-151 dimension visualization of the separation of cells within the different clusters computed using tSNE 45 . 152 This visualization shows that each cluster forms a separate group. The second tSNE dimension separates 153 the cells based on their dendritic stratification peak so that OFF-cells (light green, dark green, black) are 154 clearly separated from ON-cells (rose, violet, purple) and cells stratifying between the ChAT-bands 155 (yellow, light orange, dark orange, red). tSNE dimension 1 separates the bistratified cells (light and dark 156 blue) from ON-cells, while dimension 3 highlights the separation of clusters within the big groups (ON,  157 OFF, bistratified, between ChAT-bands). 158 159 Figure 6 shows the dendritic density distribution and example cells for the resulting 12 putative retinal 160 ganglion cell types, together with 3 example cells from each cluster. Numbers indicate the percentage of 161 retinal ganglion cells for each circuit that were grouped into each cluster as well as absolute numbers of 162 cells in the cluster. We found three distinct groups of cell types: 6 types that send information mostly to 163 the parabigeminal circuit, 3 clusters that are almost exclusively part of the pulvinar circuits, and 3 types 164 that are shared by the two circuits. Taken together, the colliculo-pulvinar and the colliculo-parabigeminal 165 circuits sample from a small and only partially overlapping set of retinal ganglion cell types. 166 The cells that are innervating predominantly the colliculo-parabigeminal circuit include six putative types: 167 cluster 1, 2, 3, 4, 7, and 12. These clusters included both bistratified types: Cluster 1 contains the CART + 168 cells and consists of rather small ganglion cells with two stratification layers that overlap with the ChAT-169 bands (n = 21; median diameter: 198 µm). These ganglion cells resemble the ON-OFF direction selective 170 cells that are CART + , co-stratify with the ChAT-bands and have relatively small dendritic fields 18 . In 171 cluster 2 we find another type of bistratified cell with a larger dendritic tree that stratifies below the ON-172 ChAT-band and above the OFF-ChAT-band (n = 10; median diameter: 214 µm). Two clusters contain 173 ON-neurons stratifying below the ON-ChAT-band. One of the ON-types (cluster 4) contains SMI32 + cells 174 (n = 22; median diameter: 276 µm), and has a morphology similar to sustained ON-alpha cells 39,40 . The 175 very strong bias of this cluster for the parabigeminal circuits mimics our antibody-labeling results of 176 SMI32 + cells ( Figure 3D and H). The second ON-type (cluster 3) does not contain SMI32 + cells, stratifies 177 further away from the ON-ChAT-band and has a smaller dendritic tree (n = 18; median diameter: 232 178 µm). A single cluster (cluster 7) has neurons stratifying between the ChAT-bands. These cells have 179 relatively small dendritic trees that are located closer to the ON than the OFF-ChAT band (n = 16; median 180 diameter: 185 µm). The last cell type that specifically targets the parabigeminal circuits consists of 181 relatively large OFF-cells stratifying far above the OFF-ChAT-band (cluster 12, n = 19; median diameter: 182 243 µm). 183 after pulvinar injections ( Figure 3D and H). The cells in cluster 8 have an exceptionally broad dendritic 189 tree and small dendritic fields (n = 8; median diameter: 199 µm). The third type of ganglion cells that 190 targets uniquely the colliculo-pulvinar circuit is a rather small OFF-type stratifying just above the OFF-191 ChAT-band (cluster 10, n = 22; median diameter: 166 µm). 192 Finally, three clusters send information to both collicular targets (cluster 5, 9 and 11). To determine if any individual cluster likely contains more than one cell type we looked at the 204 stratification and size variances within each group. This might be the case as to cluster the retinal 205 ganglion cells we only considered differences in the depth profile of their dendritic trees, but not details of 206 the xy-morphology such as dendritic field size. The dendritic field size can vary substantially between 207 cells of a given cluster ( Figure 7B), where generally smaller cells have a narrower range of dendritic 208 diameters (e.g. cluster 6 and cluster 10), while larger cells span a broader range of sizes (e.g. cluster 5 and 209 cluster 12). To determine if this variability is comparable to that of other cell types we compared it to data 210 from 8 parvalbumin-positive ganglion cells 47 . We found that both the median size and variability 211 corresponds to the observed range of dendritic tree sizes ( Figure 7C). Both the range of sizes of 212 stratification-and size-matched pairs is comparable between our dataset and the parvalbumin-cells as well 213 as the trend of increasing variability for cells with bigger dendritic trees. 214 To further investigate that the differences in size within a cluster are within the expected range, we 215 compared the size distribution of alpha-cell clusters with those previously reported 39,40 . When 216 considering all 301 labelled cells, we find that cells in the central retina tend to be smaller than in the 217 periphery ( Figure 7D). This is consistent with the observation that cells in the central mouse retina are 218 more densely packed than in the periphery 39,48,49 . Additionally, sustained alpha-cells have been show to 219 have a distinctive retinotopic size distribution 39 . We found in our data set that putative sustained alpha-

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We used transsynaptic viral tracing to investigate the rules by which visual features extracted by the retina 232 are routed in two neuronal circuits passing through the superior colliculus. We found that the two circuits 233 sample from a limited and only partially overlapping set of retinal output neurons ( Figure 6). These 234 results support the notion that, in the superior colliculus, neural circuits are based on a dedicated set of 235 connections between specific retinal output neurons and different collicular output pathways. 236 Clustering of morphological and molecular marker parameters of retinal ganglion cells lead us to three 237 main conclusions. First, our data suggests that the colliculo-parabigeminal and colliculo-pulvinar circuits 238 together receive inputs from 12 different ganglion cell types ( Figure 6). Second, we observed a clear 239 segregation in the retinal ganglion cell types providing input to the two circuits. Six of the twelve putative 240 ganglion cell types showed a strong preference for the parabigeminal circuit, and three clusters a strong 241 bias for the pulvinar circuits ( Figure 6 and Table 1). This finding indicates that the two circuits sample, at 242 least partially, from different aspects of the visual scene. Finally, there is a set of 3 visual features that 243 provide input to both circuits. 244 We used a combination of morphological and molecular cues to link the 12 clusters to known retinal 245 ganglion cell types ( compared the morphologystratification and sizewith known genetically, morphologically and 249 functionally defined cell-types. Based on these criteria, the second bistratified cluster 2 is most similar to 250 recently identified ON vertical orientation-selective neurons 50 . A second cluster with striking anatomical 251 characteristics is cluster 8, containing cells that resemble the "W3" cell, otherwise known as the "local-252 edge detector" or "object motion selective" cell 29,33,47,51 . The small, dense OFF-cells in cluster 10 have a 253 passing resemblance to horizontal OFF orientation-selective neurons 52 . There are three additional clusters 254 that resemble cell types described by Sümbül  The fourth alpha-type, the transient OFF-alpha cells (cluster 9), have been shown to selectively respond to 269 approaching stimuli 46 . Due to their resemblance to the local-edge / object-motiont detector 17,51 , cells in 270 cluster 8 most probably send information about local motion to the superior colliculus. Finally, two cell 271 types in our dataset are potential orientation-selective cells, with a preference for vertical objects for cells 272 in cluster 2 50 and for horizontal objects in cluster 10 52 . 273 If we consider the putative ganglion cell types of each circuit separately, we find that the pulvinar circuit 274 receives input from neurons with smaller dendritic fields that tend to stratify closer to the OFF-ChAT-275 band (Figure 2). Dendritic size is closely related to receptive field size and we see a similar preference for 276 small, local stimuli in the putative functional ganglion cell types that were selectively labelled in pulvinar 277 experiments (cluster 6 and 8). This finding is also in accordance with the stimulus preferences of 278 pulvinar-projecting neurons in the superior colliculus 15,55 . The parabigeminal circuit, on the other hand, 279 samples more evenly from ON, OFF and ON-OFF neurons with a larger average dendritic field (Figure 2). 280 In agreement with the morphological data, the putative functional ganglion cell types that were 281 specifically labelled in parabigeminal experiments inform this circuit about larger moving objects and 282 their movement direction (cluster 1 and 4). It is noteworthy that both circuits receive input from transient 283 OFF-alpha cells which are known to preferentially respond to expanding stimuli. Such a stimulus would 284 be created, for instance, by an approaching predator. This is in accordance with robust responses to such 285 expanding stimuli in both pulvinar-projecting 55 and parabigeminal nucleus-projecting neurons 26 of the 286 superior colliculus. 287 There are some limitations to our study. First, the rabies virus might have a bias in its infection of 288 different cell types. To mitigate this, we expressed the TVA-receptor in collicular neurons and coated the 289 rabies virus with its ligand EnvA. This approach should decrease biological variability in infection rates 56 . 290 The fact that we sample from different ganglion cell types and with very different distributions in both 291 experimental paradigms speaks against a strong infection bias of the herpes-simplex or rabies virus. 292 Another bias may arise from the injection locations and the choice of ganglion cells that we imaged. We 293 do not know the retinotopic location of the first injection into the pulvinar or the parabigeminal nucleus. 294 However, in most retinas, a large proportion of the retina contained labelled cells and our dataset contains 295 cells from all retinal quadrants and eccentricities ( Figure 2D-F)

Rabies virus production 330
Rabies production method was similar to previously published methods 61,62 . Glycoprotein G-coated, G-331 deleted B19 rabies virus (G-coated SAD-ΔG-GCaMP6s RV) was amplified in B7GG cells, which express 332 rabies glycoprotein G. For amplification, approximately 10 6 infectious units of G-coated SAD-ΔG-333 GCaMP6s RV were used to infect five 10-cm plates of 80% confluent B7GG cells followed by 2-6 hours 334 of incubation. Then, infected B7GG cells were treated with 0.05% trypsin and split into twenty-five 10-335 cm plates. To harvest the virus, we collected the supernatant of the infected cells every 3 days. 5-6 336 harvests were performed. To concentrate the virus, the supernatant was firstly centrifuged at 2,500 RPM 337 and filtered (VWR, 514-0027) to get rid of the cell debris. Then the virus was spun in an ultracentrifuge 338 for 5-12 hours at 25,000 RPM and at 4°C. After ultracentrifugation, the supernatant was discarded and the 339 pellet was dissolved in 200 µl of the original cell culture supernatant. The virus was tittered by counting a 340 culture of infected BHK cells. To produce EnvA-coated SAD-ΔG-GCaMP6s RV, approximately 10 6 341 infectious units of G-coated SAD-ΔG-GCaMP6s RV were used to infect BHK-EnvA cells. The same 342 procedure as for the G-coated RV amplification was then applied. EnvA-coated SAD-ΔG-GCaMP6s RV 343 was tittered by infection of HEK293T-TVA cells. The titer used for injection ranged from 10 7 to 10 9 344 infectious units/ml (IU/ml). 345

Surgical procedures 346
Animals were quickly anesthetized with Isoflurane (Iso-vet 1000mg/ml) and then injected with a mixture 347 of Ketamine and Medetomidine (0.75 mL Ketamine (100 mg/mL) + 1 mL Medetomidine (1 mg/mL) + 348 8.2 mL Saline). Mice were placed in a stereotaxic workstation (Narishige, SR-5N). Dura tear 349 (NOVARTIS, 288/28062-7) was applied to protect the eyes. To label the ganglion cells in the 350 parabigeminal nucleus circuit, we performed the surgery on wild type mice and injected herpes-simplex-351 virus (HSV, hEF1a-TVA950-T2A-rabiesG-IRES-mCherry, MIT viral core, RN714) and EnvA-coated 352 SAD-ΔG-GCaMP6s RV. In our experiment, we used PV-Cre mice as wild type mice. For the first 353 injection of HSV into the parabigeminal nucleus, we used micropipettes (Wiretrol® II capillary  adjusted the coordinates for each mouse according to their bregma-lambda distance. To label the injection 360 sites, DiD (Thermo, D7757) was used to coat the pipette tip. We injected in total 100-400 nl HSV in 361 single doses of up to 200 nl with a waiting time of 5-10 min after each injection. Twenty-one days later, 362 we injected rabies virus (EnvA-coated SAD-ΔG-GCaMP6s) into the superior colliculus using the same 363 method as for the HSV injections. The retinotopic location of the first injection into the parabigeminal 364 nucleus or the pulvinar is unknown. To maximize the labelling of ganglion cells in the retina, we thus 365 covered as much as possible of the superficial layer of the superior colliculus during the second injection. 366 We injected 100-200 nl of rabies virus at a depth of 1.8 mm at 4 different locations within a 1 mm 2 field 367 anterior of lambda and starting at the midline. 368 To label the pulvinar circuit, we performed the surgery on Ntsr1-GN209-Cre mice in combination with a 369 conditional HSV (hEF1a-LS1L-TVA950-T2A-RabiesG-IRES-mCherry, MIT viral core, RN716) and 370 EnvA-coated SAD-ΔG-GCaMP6s RV. The injection into pulvinar and superior colliculus were the same 371 as described for the parabigeminal nucleus. The injection coordinates for the pulvinar in a 4 weeks old 372 mouse with a bregma-lambda distance of 4.7 mm were AP: -1.85; ML: ±1.50; DV: 2.50 mm. 373 Following injection, the wound was closed using Vetbond tissue adhesive (3M,1469). After surgery, mice 374 were allowed to recover on top of a heating pad and were provided with soft food and water containing 375 antibiotics (emdotrim, ecuphar, BE-V235523). 376

Morphology of individual ganglion cells 448
The confocal Z-stacks were down-sampled and thresholded. The position of the ChAT-planes was 449 extracted and used to warp both the ChAT-signal as well as the binary Z-stack of the labelled cell. Then, 450 dendrites from other cells, noise, and axons were removed and the position of the cell body was measured. 451 The resulting warped dendritic tree was used for further analysis such as computation of the dendritic 452 profile and area measurements. All scripts can be found on github (https://github.com/farrowlab/). 453 Down-sampling and binarization: The confocal Z-stacks of individual ganglion cells were denoised using 454 the CANDLE package for MATLAB 64 and down-sampled to have a resolution of XYZ = 0.5 x 0.5 x 455 (0.25 to 0.35) µm per pixel and saved as MATLAB files. We then manually selected a threshold to 456 transform the GFP-signal (i.e. the labelled cell) into a binary version where the whole dendritic tree was 457 visible but noise was reduced as much as possible using an adapted version of the method described in 458 33,34 . 459 Extraction of ChAT-positions: ChAT-band positions were either extracted manually or automatically 460 using a convolutional neural network. For manual extraction, the ChAT-signal was smoothed using a 461 two-dimensional standard-deviation filtering approach in the XY plane with a size of 21 x 21 pixels. The 462 resulting Z-stacks were loaded into Fiji 65 . ChAT-band positions were marked as described in 33 . Briefly, 463 we labelled points in the ON-and OFF-band with an approximate spacing of 20 µm in X-and Y-direction. 464 For automated labelling, an end-to-end 3D Convolutional Neural Network called V-Net with a Dice Loss 465 Layer 66 was trained on noisy greyscale images of ChAT-images, to denoise and remove any cell bodies, 466 creating a probability map of background and foreground, with foreground being voxels that might 467 belong to the ChAT-bands. Two smoothness-regularized-least squares surfaces were fitted to manually 468 labelled data to train the algorithm and to create ground truth binary masks. Then, Otsu's thresholding 469 method combined with connected component analysis was performed on the resulting probability map to 470 automatically locate the points that belong to the ChAT-bands in new data-sets. Finally, two surfaces 471 were independently fit to the corresponding data points to approximate the two ChAT-bands 472 (https://github.com/farrowlab/ChATbandsDetection). 473 Warping: An adapted version of the code published in Sumbul et al. 2014a was used to warp the GFP-474 signal. Briefly, the ChAT-band locations were used to create a surface map, which then was straightened 475 in 3D-space. Then, the thresholded and binarized GFP-signal was warped accordingly. 476 Soma position and removal of noise: After warping, the soma position was determined by filtering the 477 GFP-signal with a circular kernel (adapted from 33 ). If this method detected the soma, it was used to 478 remove the soma from the GFP-data and the center of mass was taken as the soma position. If this 479 automated metod failed, the soma position was marked manually. Afterwards, dendrites of other cells, 480 axons, and noise were removed manually: The warped GFP-signal was plotted in side-view and en-face 481 view in MATLAB and pixels belonging to the cell were circled manually. 482 Computation of the dendritic profile and area: The distribution of the cell's dendritic tree was computed 483 as described in Sumbul et al. 2014a. Briefly, the Z-positions of all GFP-positive pixels were normalized 484 to be between -0.5 and 0.5. Then the Fourier transform of an interpolating low-pass filter was used to 485 filter the Z-positions. This resulted in a vector containing the distribution of pixels in the Z-direction. If 486 necessary, this profile was used to manually remove remaining axonal or somal pixels. In this case, the 487 dendritic profile was computed again after cleaning of the data. The area of the dendritic tree was 488 approximated by computing a convex hull (regionprops function in MATLAB). When diameters are 489 given, they were calculated as D = 2*(area / π) 1/2 . 490 Down-sampling of dendritic tree for plotting: For en-face plots of the dendritic arbor, they were down-491 sampled by calculating the local neighborhood median of all labelled pixels in patches of 50 x 50 pixels 492 and with a sliding window of 10 pixels. 493

Clustering of retinal ganglion cell morphology 494
Affinity-propagation clustering: The dendritic stratification profiles of 301 ganglion cells were smoothed 495 with the MATLAB function movmean (moving average with sliding window of 5 data points 496 corresponding to 1.7 a.u. in stratification depth). The profiles of manually identified bistratified cells were 497 set to negative values. The median dendritic profile of cells for which the molecular identity was known 498 (SMI32 or CART), was calculated (4 different SMI32 cell types, 1 CART). Then the 5 first principle 499 components of those medians and of the dendritic profiles of cells without known molecular identity were 500 computed using sparse PCA (http://www2.imm.dtu.dk/projects/spasm/) and the similarity matrix of these 501 principle components was calculated using the pdist function of MATLAB using Euclidean distance. 502 Affinity-propagation (apcluster function in MATLAB) was used to cluster the similarity matrix with 503 different preference values ranging from -1 to 0.6. The preference value for the 5 cluster centers based on 504 SMI32-and CART-positive cells was always set to 1. Cells with known molecular identity were assigned 505 to the clusters to whose median they contributed. Three validation indices (Calinski-Harabasz, Silhouette, 506 Davies-Bouldin) were computed using the evalclusters function in MATLAB, normalized, and their 507 median was used to determine the optimal preference value. 508 tSNE visualization: For visualization of the clustering result, we generated a five-dimensional non-linear 509 embedding of the cells using t-distributed Stochastic Neighbor Embedding, tSNE 45 . We used the 510 smoothed dendritic profiles as input data, used cosine as a distance measurement, and set the number of 511 PCA dimensions, which are calculated in a first step, to 25. For the graph in this paper, we show 512 comparisons of the resulting tSNE dimension 1, 2, and 4. 513

Size distribution analysis 514
Comparison to PV cells: For size distribution comparisons, we used previously published data from 8 515 different types of parvalbumin-positive (PV) ganglion cells 47 . For each of our 12 clusters, we looked for a 516 PV-type with a similar stratification depth and average dendritic field size. If there was such a PV-type, 517 we calculated the median and quartiles of the dendritic field diameters of all cells of this type and 518 compared it to our data. 519 Retinotopic size distribution: For retinotopic size distribution calculations, we computed a moving 520 median diameter within a circular window of 250 µm radius, moving by 100 µm. The resulting 50 x 50 521 median size matrix was convolved with a gaussian with sigma = 200 µm (using MATLAB function 522 fspecial and nanconv). 523

Quantification of SMI32+ cells and CART+ cells 524
Numbers of double-labelled cells: To quantify the number of double-positive cells for CART/GCaMP6s 525 and SMI32/GCaMP6s, we scanned a z-stack (1 to 5 µm Z-resolution) of the whole retina using the 526 confocal microscope with an 10x objective. Images of the anti-CART or SMI32 and the anti-GFP staining 527 were opened in Fiji. For counting CART + cells, cells were marked using the point tool and counted 528 manually. Note that the anti-CART antibody also labels a group of amacrine cells, therefore the complete 529 Z-stack should be checked for each CART + cell to make sure that the labelling truly overlaps with the 530 anti-GFP signal. The CART expression pattern was consistent with previous reports 67 . In total we 531 counted 3 retinas for parabigeminal experiments and 6 retinas for pulvinar experiments. For counting 532 SMI32 + cells, cells were counted manually using the cell counter plugin. In total we counted 3 retinas for 533 parabigeminal experiments and 4 retinas for pulvinar experiments. 534 Numbers of cells for types of alpha cells: To test which of the four alpha cell types were part of each 535 circuit, we acquired small high-resolution Z-stacks (2.5 µm/pixel) of XY = 103 x 103 µm size (128 x 128 536 pixel, 63x objective) covering the full depth of the dendritic tree and centered around the soma of 91 537 SMI32 + / GCaMP6s + cells in n = 3 retinas from parabigeminal experiments and 90 SMI32 + / GCaMP6s + 538 cells in n = 3 retinas from pulvinar experiments. We plotted top and side views of each Z-stack in 539 MATLAB and manually decided for each cell if it was a sustained ON-alpha cell (dendrites below the 540 ON-ChAT band), a transient ON-alpha (dendrites just above the ON-ChAT band), a transient OFF-alpha 541 (dendrites just below or on the OFF-ChAT band) or a sustained OFF-alpha cell (dendrites above the 542 OFF-ChAT band). 543