The Foveal Visual Representation of the Primate Superior Colliculus 1,2 3 4 1,2* 2 Chih-Yang Chen , Klaus-Peter Hoffmann , Claudia Distler , Ziad M

bioRxiv preprint doi: https://doi.org/10.1101/554121; this version posted February 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

1 The foveal visual representation of the primate superior colliculus 1,2 3 4 1,2* 2 Chih-Yang Chen , Klaus-Peter Hoffmann , Claudia Distler , Ziad M. Hafed

1 3 Werner Reichardt Centre for Integrative Neuroscience, Tuebingen University, Tuebingen, 4 Germany. 2 5 Hertie Institute for Clinical Brain Research, Tuebingen University, Tuebingen, Germany. 3 6 Research Department of Neuroscience, Ruhr University Bochum, Bochum, Germany. 4 7 Department of General Zoology and Neurobiology, Ruhr University Bochum, Bochum, 8 Germany. 9 *Correspondence to: [email protected] 10 11 12 13 Abstract 14 Processing of foveal retinal input is important not only for high quality visual scene analysis, but

15 also for ensuring precise, albeit tiny, gaze shifts during high acuity visual tasks. The

16 representations of foveal retinal input in primate lateral geniculate nucleus and early visual

17 cortices have been characterized. However, how such representations translate into precise eye

18 movements remains unclear. Here we document functional and structural properties of the foveal

19 visual representation of midbrain superior colliculus. We show that superior colliculus,

20 classically associated with extra-foveal spatial representations needed for gaze shifts, is highly

21 sensitive to visual input impinging on the fovea. Superior colliculus also represents such input in

22 an orderly and very specific manner, and it magnifies representation of foveal images in neural

23 tissue as much as primary visual cortex does. Primate superior colliculus contains a high-fidelity

24 visual representation, with large foveal magnification, perfectly suited for active visuomotor

25 control and perception.

26 27

28 Introduction 29 A defining feature of our visual system is its foveated nature. A tiny portion (~1-2%) of our

30 retina, fovea, contains the highest density of photoreceptors (1) while, at the same time,

31 commanding large neural tissue magnification as signals traverse from retina to lateral geniculate

32 nucleus and primary visual cortex (V1) (2). Such magnification confers on foveal visual input a

33 tremendous computational advantage compared to images sampled outside fovea. As a result, we

34 frequently move our eyes to align tiny portions of our visual environment with our fovea; fovea

35 represents the “origin” of our visual space, and most of our visually-guided eye-movement

36 behavior (e.g. during reading, sewing, driving) involves aligning this “origin” with what

37 currently matters most.

38 Despite the importance of foveal visual processing, and despite the suitability of primate

39 models for investigating it (3-11), studies of foveal visual mechanisms have become increasingly

40 rare in the past 3-4 decades. This is primarily due to challenges associated with studying foveal

41 vision: individual retinal ganglion cells in the foveal representation often have response fields

42 (RF’s) that are the size of single photoreceptors (6, 12); thus, even tiny fixational eye movements

43 can displace images away from RF’s. Paradoxically, a historical shift towards studying extra-

44 foveal eccentricities in perception and cognition was simultaneously accompanied (13) by an

45 assumption that fixational eye movements in between gaze shifts are irrelevant. Because we now

46 know that this is an oversimplification (13, 14), there is an ever-pressing need to investigate

47 foveal processing mechanisms, even in the presence of active fixational gaze behavior.

48 Such a need is especially relevant for sensory-motor areas, like midbrain superior

49 colliculus (SC), that are at the nexus of both visual processing and eye movement generation.

50 The SC is instrumental for generating microsaccades (15), which precisely re-direct gaze during

51 foveal vision (16), and which also influence peripheral eccentricities (14, 17). However, it is not

52 known how microscopic gaze control can be guided visually; the SC’s foveal visual

53 representation is unexplored. In fact, countless debates have existed about whether foveal

54 information is directly routed from retina to SC (5, 18-23). Nowadays, a prevailing assumption is

55 that foveal vision is the domain of retino-geniculate pathways, whereas extra-foveal event

56 detection for gaze shifts is the purview of SC (24, 25). This dichotomy gained even more traction

57 when it was suggested that the “foveal” zone of “motor” SC is a distinct “fixation” zone

58 preventing, rather than generating, eye movements (26).

59 Regardless of its source, primate SC does possess a visual processing machinery (9, 23,

60 25, 27-31) capable of modulating cortical areas (32) and influencing eye movements (30). Our

61 purpose here is to characterize the physiological and structural properties of foveal vision in SC;

62 we show that SC is as foveal a visual structure as V1.

64 Results

65 Primate superior colliculus is highly sensitive to foveal visual input

66 We recorded from 413 neurons isolated and characterized online in awake macaque monkeys N

67 and P. We characterized RF hotspot location (the point for which maximal visual response was

68 evoked), RF area, and other visual response properties by presenting small spots of light over an

69 otherwise uniform gray background, and we carefully controlled for image shifts caused by

70 incessantly occurring fixational eye movements (Materials and Methods).

71 We first identified SC sites containing neurons sensitive to foveal visual stimuli. Figure

72 S1A, B (left column) shows that RF hotspots <1-2 deg in eccentricity tiled the entire foveal

73 region contralateral to the recorded SC. This was also true for anesthetized monkeys R and F,

74 recorded in separate experiments (Fig. S1A, B, right column; Materials and Methods). Therefore,

75 primate SC has clear access to foveal visual input.

76 We examined foveal visual RF’s in the awake animals by plotting peak stimulus-evoked

77 response as a function of stimulus location, depicted in polar coordinates (Fig. 1A, top row

78 showing 4 example neurons). We observed small, punctate visual RF’s having high sensitivity.

79 All 4 neurons in Fig. 1A had RF’s almost entirely contained within the rod-sparse foveola region

80 of the retinal image (i.e. with eccentricities <0.5 deg), suggesting access to the highest acuity

81 portion of visual input. The middle row of Fig. 1A plots the same visual RF’s using log-polar

82 coordinates (15) to magnify small eccentricities, and it demonstrates that despite the proximity of

83 all neural RF’s to gaze line of sight, the inner borders of all RF’s were very well defined. Thus,

84 SC foveal visual RF’s sample highly specific regions of the visual image, even within foveola.

85 Foveal SC neurons were also particularly light-sensitive, reaching strong peak visual

86 responses of several hundreds of spikes/s (Fig. 1A, bottom row; each spike raster shows

87 responses form an individual trial, and the stacked trials show responses from the 25 nearest

88 locations to each neuron’s RF hotspot). The particular neurons shown in Fig. 1A had zero

89 baseline activity (typical of foveal and extra-foveal SC neurons; Fig. S2A), and only responded

90 when light impinged on a small region within fovea. Their high sensitivity was consistent across

91 the population (Fig. S2B), and it was similar to sensitivity in more eccentric neurons (e.g. 8-10

92 deg in Fig. S2B). Thus, SC not only has access to even foveolar (i.e. rod-sparse) image regions,

93 but it is also highly sensitive to them.

95 Figure 1 Foveal visual neurons of primate superior colliculus (SC). (A) Four example neurons recorded from right 96 SC in awake monkeys. Top: visual response fields (RF’s) in polar coordinates (Materials and Methods). Middle: same 97 RF’s using log-polar coordinates magnifying small eccentricities (15). Bottom: raw firing rates (blue) along with 98 s.e.m. error bars (dashed blue) when a stimulus was presented near the neuron’s RF hotspot (Materials and Methods). 99 Individual rasters show raw spike (action potential) times across repetitions of stimulus presentation. All neurons had 100 RF’s almost entirely contained within the rod-sparse foveola region (i.e. <0.5 deg eccentricity; (6-8)). Different 101 neurons tiled different portions of foveal space (top two rows), and all had strong sensitivity. (B) Across both right 102 and left SC’s, the entire foveal space was represented. Each small circle indicates RF hotspot location from an example 103 neuron, and solid lines indicate RF inner boundaries. (C) Foveal RF’s were much smaller than peripheral ones. Six 104 example neurons with RF boundaries and hotspot locations indicated by outlines and small circles, respectively. Right: 105 log-polar coordinates magnifying the small, but highly well-defined visual RF’s of the foveal neurons. Also see Fig. 106 2A. 107

108 Strong visual sensitivity was additionally reflected in neural response latency (29-31):

109 first-spike latency (Materials and Methods) was similar to that in peripheral neurons (Fig. S2C).

110 Only in superficial SC layers, response latency decreased with increasing eccentricity within the

111 central 2 deg (Fig. S2C, blue). Because superficial neurons, but not deeper ones, receive direct

112 retinal input (3-5), this non-uniformity could reflect the sparseness of rod photoreceptors (having

113 fast integration times) in foveola.

114

115 Foveal superior colliculus samples visual space non-uniformly, even within foveola

116 The fact that foveal SC neurons have well-defined RF’s (Fig. 1A) suggests that the population as

117 a whole can achieve full coverage of foveal image regions. We observed this not only in hotspot

118 locations (Fig. S1), but also when we examined individual RF areas (Fig. 1B). Our recorded

119 neurons exhibited classic hallmarks of population coding: tiling of space in terms of hotspot

120 location as well as RF overlap, much like saccade-related activity for much larger eccentricities

121 (33).

122 We were particularly interested in the dependence of such foveal population coding on

123 eccentricity. It is known that RF area increases with eccentricity (Fig. 1C) (9, 31), like in visual

124 cortices (34), but it is also assumed that spatial resolution in visual cortices is uniform within the

125 foveal image representation (34). This is not what we found. There was clear dependence of RF

126 area on eccentricity even within foveal eccentricities (Fig. 2A, left, awake animals). Moreover,

127 this dependence followed a consistent supra-linear relationship with extra-foveal neurons (Fig.

128 2A, right, each dot is a neuron). Therefore, there exists a continuum of SC visual representation,

129 from well-within the rod-sparse foveolar region up to eccentricities two orders of magnitude

130 larger. This non-uniformity of spatial sampling even within fovea also explains why

131 microsaccades are needed to re-align gaze (16): tiny microsaccade-induced image displacements

132 equivalent to a mere handful of individual foveal photoreceptors are sufficient to bring images of

133 fine stimuli onto SC RF’s with higher spatial resolution (smaller area) than before the eye

134 movements.

135

136 Figure 2 Non-uniform foveal spatial sampling by SC. (A) Left: visual RF area as a function of eccentricity (awake 137 monkeys N and P). RF area depended on eccentricity (p=0.044, 1-way ANOVA, F=2.782, n=121 neurons). Right: RF 138 areas from both foveal and eccentric neurons (dots) together. Foveal neurons (e.g. < 2 deg, dashed line) formed a 139 continuum with peripheral ones. (B) Non-uniform spatial sampling even within individual RF’s. We binned neurons 140 according to their preferred eccentricity (color-coded). For each bin, we plotted 1-dimensional normalized RF profiles 141 along the radial axis connecting gaze center to RF hotspot (inset; Materials and Methods). Eccentric neurons (e.g. 142 right panel) had symmetric RF’s. Foveal neurons became increasingly skewed with decreasing eccentricity; there was 143 no activity beyond the 0-deg singularity towards the ipsilateral visual field. Each curve shows average normalized 144 firing rate from all neurons within a given eccentricity bin, along with s.e.m. across neurons. Fig. S1 shows raw foveal 145 hotspot locations. (C) Top row: RF skewness quantified as the ratio of a-to-b (inset; Materials and Methods). Foveal 146 neurons (left) had skewed RF’s (p=3.797x10-5, Wilcoxon signed rank test against a median of 1); eccentric neurons 147 (right) did not (p=0.906, Wilcoxon signed rank test against a median of 1). Bottom row: c-to-d ratios for the same 148 neurons (i.e. the RF profiles along the direction dimension at the RF hotspot eccentricity; inset; Materials and 149 Methods). Both foveal (p=0.504) and eccentric (p=0.367) neurons did not show significant RF skewness in the 150 direction dimension. Solid colored lines indicate median values across the population. 151

152

153 We also confirmed the results of Fig. 2A in anesthetized monkeys, from which we

154 recorded the most superficial SC visual laminae (Fig. S3; Materials and Methods). Additionally,

155 because deeper SC layers exhibit saccade-related activity, we expected microsaccade-related

156 activity (15) to emerge in the awake animals below foveal visual neurons; this was indeed the

157 case (Fig. S4). It was also the case that microsaccade-related movement fields sampled foveal

158 space non-uniformly like the visual RF’s (Fig. S5), but the movement fields were smaller. In all

159 analyses, here and elsewhere, relevant statistics are shown in respective figure legends.

160

161 Foveal superior colliculus exhibits strict spatial cut-offs in representing contralateral and

162 ipsilateral visual eccentricity

163 Non-uniformity of SC spatial sampling within foveal eccentricities was not restricted to RF

164 areas. Even individual RF’s were often strongly skewed. For example, the RF of Neuron #1 in

165 Fig. 1A (top row) had a longer activity tail at eccentricities larger than RF hotspot location

166 compared to smaller. We characterized such skewness by plotting RF profiles along a single

167 dimension (eccentricity) connecting the line of sight to a given neuron’s RF hotspot (Fig. 2B,

168 inset), and we classified neurons according to their preferred eccentricities (Fig. 2B, different

169 colors). Extra-foveal neurons were largely symmetric along the eccentricity dimension (Fig. 2B,

170 right, showing example neurons representing 8-10 deg). However, as RF location approached the

171 discontinuity of “zero” eccentricity in the fovea, there was increasing RF skewness (Fig. 2B, left;

172 compare activity beyond versus nearer than the preferred eccentricity eliciting maximal response

173 in each curve). On the inner edges of RF’s, there was an extremely strict cutoff of neural activity,

174 such that there was no activity on the other side of the “zero” deg discontinuity (ipsilateral to the

175 recorded SC). This happened even if it meant strong RF skew (e.g. Fig. 2B, left, blue). Even

176 neurons with <0.2 deg preferred eccentricity (Fig. 2B, left, blue) were strictly contralateral (any

177 residual ipsilateral activity on the other side of “zero” was due to visual activation by the fixation

178 spot itself, as in Fig. 5 below, or unavoidable residual eye-position calibration/correction errors).

179 These results are consistent with a “split fovea” representation (18, 35).

180 We quantified RF skewness by measuring distance a from RF hotspot location to RF

181 outer border and comparing it to distance b from RF hotspot location to RF inner border (Fig.

182 2C, top inset). Foveal SC neurons were significantly skewed (Fig. 2C, top left, a-to-b ratio>1)

183 when compared to extra-foveal neurons (Fig. 2C, top right, a-to-b ration=1). Such skewness was

184 restricted to the eccentricity dimension because measuring RF’s along an axis orthogonal to

185 eccentricity (Fig. 2C, bottom inset) revealed clear symmetry whether the neurons were foveal

186 (Fig. 2C, bottom left) or extra-foveal (Fig. 2C, bottom right). Therefore, foveal SC visual

187 responses are strongly lateralized along the eccentricity dimension.

188

189 Superior colliculus possesses orderly topographic representation of foveal visual space

190 Computational models of anatomical topography (36) suggest that RF skewness (Fig. 2) is a

191 hallmark of foveal magnification. We therefore next turned to the question of how SC foveal

192 vision is structurally represented. In anesthetized animals (Materials and Methods), we densely

193 recorded the most superficial SC laminae (putatively, the retina-recipient neurons). We then

194 sacrificed the animals and carefully registered our dense recordings with structural

195 neuroanatomy (Fig. S6, Movies S1-S2, and Data Table S1; Materials and Methods). We assessed

196 preferred eccentricities along SC surface (Fig. 3A, showing a top-down view; each gray dot is an

197 SC electrode location, Materials and Methods). We plotted iso-eccentricity lines (color-coded)

198 and found orderly SC topography even within the foveal representation. The orderly eccentricity

199 organization was also continuous with extra-foveal eccentricities (Fig. 3A; thick red lines show

200 iso-eccentricity lines in our model of SC topography, Fig. 3C). In this analysis, we were careful

201 to obtain a view of SC similar to that used in previous estimates (37) of SC topography that were

202 based on evoked saccades after electrical microstimulation of the deeper layers. This allowed us

203 to directly compare our data, containing explicit measures of foveal topography, to a classic

204 model (37) only extrapolating from extra-foveal (and saccadic) measurements. We also repeated

205 the same analysis for iso-direction lines relative to the horizontal meridian (Fig. 3B). Finally, we

206 confirmed that we could still find evidence of orderly topography even in our awake animals,

207 recorded with single-electrode penetrations from session to session (Fig. S7).

208 Therefore, foveal SC representation not only does exist (Fig. 1), but it is also organized in

209 highly specific manners, both functionally (Fig. 2) and structurally (Fig. 3).

210

211 Figure 3 SC is as strongly foveally magnified as primary visual cortex (V1). (A) Using dense superficial SC sampling 212 (anesthetized monkeys R and F), we estimated iso-eccentricity lines for right SC. Gray circles denote electrode 213 locations (Materials and Methods; Fig. S6). We drew interpolated lines (color-coded) along which neurons preferred 214 a single eccentricity. Foveal eccentricities were anatomically represented in an orderly manner at the rostro-lateral 215 pole (see the 0.5, 1, and 2 deg iso-eccentricity lines). Thick red lines show iso-eccentricity lines in our mathematical 216 model of SC surface topography (Materials and Methods; C). (B) Similar analyses for iso-direction lines. (C) Our SC 217 surface topography model. The red arrow indicates 2-deg eccentricity; almost 1 mm, or approximately 1/4-1/3, of SC 218 tissue space (along the horizontal meridian) is foveal. Data Table S1 shows SC surface topography in three- 219 dimensional anatomical coordinates. (D) The universally accepted model (37), aligned at the same origin, assumes 220 much smaller foveal magnification (blue map; blue arrow indicates 2-deg eccentricity). (E) Linear tissue 221 magnification factor (10, 39) along the horizontal meridian. Our data (red) demonstrate larger than two-fold foveal 222 magnification (vertical red arrow). (F) Our magnification factor curve (plotted in red as “inverse magnification factor” 223 (11), in order to facilitate comparison to the other shown data) was similar to V1 foveal magnification factor (black). 224 Note that we corrected for anatomical size differences between SC and V1 before performing this comparison to V1 225 (Materials and Methods). Our data (red) is superimposed on a meta-analysis adapted, with permission, from (11). 226

227

228 Superior colliculus magnifies foveal visual representation in neural tissue as much as

229 primary visual cortex (V1)

230 Our dense mappings of Fig. 3A, B, coupled with strong RF skewness (Fig. 2), convinced us that

231 SC contains significantly larger foveal magnification than we had anticipated. We therefore

232 fitted our data from Fig. 3A, B (color-coded lines) with a mathematical function incorporating

233 foveal magnification (Fig. 3A, B, thick red lines), similar to past descriptions of V1 and SC

234 (Materials and Methods). Our data fits (Fig. 3C) revealed that the 2-deg eccentricity line was

235 located up to almost 1 mm away from the rostro-lateral “origin” of the topographic map (Fig. 3C,

236 red arrow); this indicates that along the eccentricity dimension, up to 1/4-1/3 of the SC represents

237 foveal eccentricities. This is larger than two-fold the magnification factor extrapolated by classic

238 SC topographic modeling (37). To demonstrate this, we aligned in Fig. 3D both our data (red) as

239 well as the original extrapolated model (37) (blue). We found a remarkable difference: what the

240 original model predicts as the 5-deg eccentricity line in neural tissue is in reality only the edge of

241 the foveal representation (2 deg).

242 We also explicitly calculated magnification factor. In Fig. 3E, we estimated linear foveal

243 magnification factor along the horizontal meridian (that is, mm of neural tissue per deg of visual

244 eccentricity) for our data (red) as well as the classic extrapolated model (37) (blue). We

245 confirmed larger than two-fold increase in foveal magnification factor in fovea compared to the

246 classic model (37). Note that both models converge at larger eccentricities because larger

247 eccentricities are logarithmically compressed.

248 We then compared our data for SC foveal magnification to V1 foveal magnification.

249 Because V1 is almost an order of magnitude larger than SC, we first scaled our SC

250 measurements to equalize for overall size (Materials and Methods). We then plotted our

251 magnification factor measurements along with an extensive meta-analysis of numerous V1

252 measurements (11) (Fig. 3F, this time plotted as “inverse magnification factor” by the authors of

253 the meta-analysis; that is, min arc of visual eccentricity per mm of neural tissue). We found that

254 SC foveal magnification is as good as V1 foveal magnification. In hindsight, this makes perfect

255 sense: if SC is to visually guide highly precise microsaccadic gaze alignment (15), it ought to

256 also have a high-fidelity visual representation.

257 An immediate functional implication of large SC foveal magnification is that small spots

258 of light presented foveally would simultaneously activate a large population of neurons.

259 Specifically, because each RF is spatially extended, a single stimulus is expected to activate

260 multiple neurons, and such activation depends on RF overlap between neurons. For example, for

261 Neurons #2 and #4 from Fig. 1, plotting their RF images in neural tissue space revealed that the

262 area occupied in anatomical space according to our topography data in Fig. 3C was greater than

263 five-fold the area predicted by the classic model of SC topography (Fig. 4A, compare right and

264 left columns; the SC was rotated here to make the eccentricity dimension horizontal in the

265 figure). This means that a small foveal spot (e.g. at 0.5 deg eccentricity) would activate an area

266 of SC neural tissue greater than five times larger than would be classically predicted (37). This is

267 significant because a well-known theoretical consequence of foveal magnification is equalization

268 of the size of the active population across eccentricities (37). With the classic model, plotting RF

269 area versus eccentricity in visual space (Fig. 4B, left) and tissue space (Fig. 4B, middle) revealed

270 that equalization across eccentricities was only partial (the slope of the regression line in Fig. 4B,

271 middle was >0), and foveal eccentricities were clear outliers. Only with the larger foveal

272 magnification factor revealed by our own SC measurements could we observe complete

273 equalization of active neural tissue (Fig. 4B, right).

274

275 Figure 4 Greater than five-fold foveal tissue area magnification than previously assumed. (A) Each row shows the 276 size of an example neuron’s visual RF in anatomical coordinates (left: classic SC model; right: model based on our 277 dense sampling). This coordinate system for displaying RF’s is equivalent to estimating the SC neural tissue area 278 activated by a stimulus (37, 40). The inset in each row shows each neuron’s visual RF in visual coordinates (as in Fig. 279 1). Our topography data (right column) demonstrate larger than five-fold active area of neural tissue for foveal visual 280 locations than the old (37) estimate (left column). This is consistent with the larger linear magnification factor in Fig. 281 3E. Note that we rotated the SC such that the representation of the horizontal meridian (tilted in anatomy; Fig. 3) is 282 now horizontal. (B) The leftmost panel shows RF areas in visual coordinates from monkey N and P (e.g. Fig. 2A). 283 The expected increase with eccentricity should be “equalized” in SC neural tissue space due to foveal magnification 284 (37, 40). However, plotting RF area in SC tissue space using the classic model (37) fails to result in equalization when 285 foveal neurons are included in analysis (positive slope in middle panel; also: p=4.851x10-8, 1-way ANOVA as a 286 function of eccentricity, F=4.13). This failure was also noted in (40). With larger foveal magnification (rightmost 287 panel; upward red arrow), such equalization is now more successful (zero slope in rightmost panel; also: p=0.025, 1- 288 way ANOVA as a function of eccentricity, F=1.77). 289

290 Our observation of larger SC foveal magnification not only clarifies issues related to

291 sensory representation across the population of SC neurons (e.g. Fig. 4), but it additionally

292 recasts interpretations of anatomical SC properties. For example, predictions on efferent

293 projections from SC to the eye muscles (for driving saccades) (38) have previously relied on the

294 classic model of SC topography. However, interpretation of the very same data would be very

295 different based on our measurements of foveal magnification (Fig. S8). It is exactly for this

296 reason that we provide Data Table S1 as a community resource for future studies of structure-

297 function SC relationships.

298

299 Fixational eye movements activate up to 1/4-1/3 of superior colliculus neural tissue by

300 foveal stimuli

301 An important additional functional consequence of large foveal magnification is that small eye

302 movements can, by virtue of moving retinal images, cause substantial variations in SC neural

303 activity. This would happen even for tiny ocular drifts occurring in between microsaccades.

304 Consider, for example, the scenario in Fig. 5A. A foveal RF has a well-defined inner border

305 represented in green (consistent with Figs. 1A, B, 2B). A small ipsiversive ocular drift (away

306 from the neuron’s RF direction; orange) would be enough to bring the image of the fixation spot

307 into the inner edge of the RF. Thus, even when no visual stimulus is presented, the neuron might

308 still be activated by the visual image of the fixation spot. Indeed, a fraction (22.3%) of our foveal

309 neurons showed variable baseline activity in the absence of visual onsets (Materials and

310 Methods). To demonstrate that this activity was visually-driven by the fixation spot itself, we

311 identified 100-ms fixation epochs not containing any microsaccades. We then carefully assessed

312 eye position in these epochs relative to the fixation spot (Materials and Methods). Example

313 Neuron #5 (Fig. 5B) had an RF hotspot location of 0.3 deg. We obtained fixation epochs and

314 sorted them based on eye position relative to the fixation spot. We also paired each epoch with

315 simultaneously recorded spike rasters (black ticks). The neuron clearly exhibited variable

316 baseline activity, which was strongest when eye position along the axis of the neuron’s RF

317 hotspot (similar to Fig. 2B analysis) was ipsiversive (that is, bringing the image of the fixation

318 spot into the RF). Thus, trial-to-trial neural variability was caused by variability of fixational eye

319 position.

320

321 Figure 5 Significant impact of ocular drifts on foveal neural variability. (A) Top: if gaze (orange) is centered on the 322 stationary fixation spot (white), a foveal RF (green) would not experience visual stimuli. Bottom: if gaze drifts by 323 <0.1 deg away from the RF location, the new RF position (moving with the eye) now experiences the fixation spot as 324 a visual stimulus. Therefore, foveal SC neuronal variability during fixation should depend on gaze. (B) Example 325 neuron (with RF hotspot eccentricity at 0.3 deg) exhibiting substantial trial to trial variability in pre-stimulus activity. 326 We analyzed eye position (blue) across trials in microsaccade-free 100-ms epochs (Materials and Methods); we sorted 327 ten example epochs based on eye position (using the conventions of A). Black rasters show corresponding neural 328 activity. The neuron was most active with eye position farthest away from the RF, consistent with A. (C) Spike- 329 triggered average eye position during baseline fixation from the same neuron (Materials and Methods). Spikes were 330 most likely within ~50-100 ms after an eye position deviation away from RF location, consistent with A. (D) Similar 331 result for a slightly more eccentric neuron; a larger ocular deviation was now needed to cause neural firing. (E) This 332 was also evident in the spike-triggered average eye position. (F) For all neurons exhibiting baseline activity, we 333 confirmed B-E by sampling the value of spike-triggered average eye position at either 0 ms (top histogram) or -50 ms 334 (bottom histogram) relative to spike onset (colored vertical lines in C, E). Spikes were consistently preceded by 335 “away” eye positions (for 0 ms: median = -0.0102, p=3.986x10-5, Wilcoxon signed rank test against 0; for -50 ms: 336 median = -0.0127, p=4.422x10-5, Wilcoxon signed rank test against 0). 337

338 We further demonstrated the dependence of neural variability on eye position in this

339 example neuron by computing spike-triggered average eye position leading up to any given spike

340 (Fig. 5C). A spike by the neuron was more likely when eye position deviated (up to ~50 ms

341 earlier) away from the fixation spot (along the RF hotspot axis, consistent with the schematic of

342 Fig. 5A). Example Neuron #6 was slightly more eccentric, and was thus activated by larger drifts

343 in eye position away from the fixation spot (Fig. 5D, E), and measures of spike-triggered eye

344 position were consistent across the population of neurons affording us this analysis (Fig. 5F).

345 Therefore, because of foveal representation and magnification, significant variability of ongoing

346 SC activity can be caused by tiny fixational gaze behavior.

347 If one were to now combine the results of Fig. 5 with those of Fig. 4, it would be possible

348 to estimate, for normal fixational gaze behavior, the amount of SC neural tissue that would be

349 activated simply when normally fixating. This amounts to almost 1/4-1/3 of the entire SC (Fig.

350 S9). Indeed, large foveal magnification makes observations of significant influences of small eye

351 movements on peripheral SC visual activity (14) reasonable.

352

353 Microsaccades are associated with pre-movement shifts in foveal superior colliculus

354 representations

355 Finally, in all of our analyses, we excluded visual onsets near the occurrence of microsaccades

356 (Materials and Methods), because these can alter foveal visual perception (17). However, we had

357 neurons in which sufficient trials with microsaccades existed, allowing us to investigate a neural

358 basis for such foveal perceptual alteration (17). We mapped visual RF’s without microsaccades,

359 and also when stimulus onset occurred <100 ms before microsaccade onset. To avoid

360 contamination by microsaccade-related motor bursts (15), we only considered ipsiversive

361 microsaccades away from RF location and not emitting an ipsiversive microsaccade-related

362 burst. Figure 6A demonstrates results from two example foveal neurons. Consistent with

363 perceptual alterations in (17), both neurons showed an ipsiversive shift in RF hotspot location

364 (i.e. in the same direction as the microsaccade (17); Fig. 6A, rightward component of red

365 arrows). Across the neurons for which we performed this analysis, there were substantial

366 momentary shifts in RF hotspot locations if stimuli appeared before microsaccades (Fig. 6B,

367 left). Interestingly, foveolar neurons always shifted ipsiversively (i.e. in the direction of

368 upcoming microsaccades), whereas more eccentric neurons tended to shift outward; such a

369 reversal with eccentricity is reminiscent of pre-microsaccadic perceptual reversals with

370 eccentricity (17). Importantly, these RF shifts were not caused by differences in eye positions

371 across the conditions (Fig. 6B, middle and right).

372 Therefore, there exist not only influences of eye position on SC neural variability due to

373 large foveal magnification (Fig. 5; Fig. S9), but microsaccades are also associated with transient

374 changes in SC’s foveal representation (Fig. 6). This supports evidence that active fixational gaze

375 behavior can have far-reaching impacts on neural activity and perception (14, 17).

376

377 Figure 6 Foveal visual RF’s shift before microsaccades. (A) Each column shows an example neuron (#7 and #8) 378 having sufficient trials with microsaccades to allow mapping the RF before their onset (Materials and Methods). The 379 top left RF map in each neuron was obtained without microsaccades (like in Fig. 1). The top right map was obtained 380 with stimuli appearing <100 ms before ipsiversive microsaccades (inset). The big panel for each neuron shows RF 381 boundaries and centers from the two conditions. We did not compare RF boundaries between conditions because of 382 limited numbers of microsaccades (Materials and Methods). However, substantial shifts in RF hotspot locations were 383 clearly evident (thick red arrows). (B) Most foveal neurons exhibited pre-microsaccadic shifts (leftmost plot with 384 black dots being the RF hotspot locations without microsaccades and connected red dots being the same neurons’ RF 385 hotspot locations before microsaccades). Because microsaccades alter eye position, we also checked whether the shifts 386 in the left panel could be explained by different eye positions at stimulus onset (middle plot). As expected (14), there 387 was a small shift in eye position before ipsiversive microsaccades (inset in the middle plot), but it was significantly 388 smaller than the RF shifts seen in the left plot. The rightmost plot summarizes the magnitude of the RF shifts (left bar) 389 or eye position shifts (right bar) with and without microsaccades. Each circle is an individual neuron (n=24). Pre- 390 microsaccadic RF shifts were larger than predicted by eye position shifts in the same trials (p=2.0706x10-5, Wilcoxon 391 signed rank test). 392

393

394 Discussion

395 Our results demonstrate that SC is as foveal a visual structure as V1 in terms of spatial sampling.

396 This not only helps explain the high precision of small eye movements (14, 16), but it can also

397 have implications on the role of ascending SC visual signals to extra-striate visual cortices (32).

398 Such ascending signals are expected to be strongly modulated by fixational eye movements

399 (Figs. 5, 6, S9) (14, 17), directly impacting how visual coding may proceed. Our topographic

400 model of SC surface is also a useful resource for further investigations of structure-function

401 relationships in the visual and oculomotor systems. For simplicity, we formulated the model

402 based on the same mathematical equations as (37), but additional variants may be envisioned,

403 such as including asymmetries in upper visual field representation (31). Anesthesia and multi-

404 unit recording of the most superficial (retina-recipient) SC laminae in our experiments (Materials

405 and Methods) reduced the chance of observing strong instantiations of these asymmetries in

406 neural RF’s. Either way, the model, along with the strict lateralization that we observed in both

407 awake and anesthetized animals (e.g. Fig. 2), also raises interesting questions on anatomical

408 interactions between the two SC’s, for example, along the vertical meridian. In reality, we think

409 that fixational eye movements very strongly reduce the likelihood of a purely vertical stimulus in

410 retinotopic coordinates. Therefore, a “split” fovea representation (18, 35) is not as problematic as

411 might appear at face value.

412 413 References 414 1. S. L. Polyak, The retina. (University of Chicago Press, Oxford, 1941).

415 2. P. Azzopardi, A. Cowey, The overrepresentation of the fovea and adjacent retina in the 416 striate cortex and dorsal lateral geniculate nucleus of the macaque monkey. Neuroscience 417 72, 627-639 (1996).

418 3. J. G. Pollack, T. L. Hickey, The distribution of retino-collicular axon terminals in rhesus 419 monkey. J Comp Neurol 185, 587-602 (1979).

420 4. P. H. Schiller, J. G. Malpeli, S. J. Schein, Composition of geniculostriate input ot 421 superior colliculus of the rhesus monkey. J Neurophysiol 42, 1124-1133 (1979).

422 5. M. E. Wilson, M. J. Toyne, Retino-tectal and cortico-tectal projections in Macaca 423 mulatta. Brain Res 24, 395-406 (1970).

424 6. C. A. Curcio, K. R. Sloan, Jr., O. Packer, A. E. Hendrickson, R. E. Kalina, Distribution of 425 cones in human and monkey retina: individual variability and radial asymmetry. Science 426 236, 579-582 (1987).

427 7. E. T. Rolls, A. Cowey, Topography of the retina and striate cortex and its relationship to 428 visual acuity in rhesus monkeys and squirrel monkeys. Exp Brain Res 10, 298-310 429 (1970).

430 8. V. H. Perry, A. Cowey, The ganglion cell and cone distributions in the monkey's retina: 431 implications for central magnification factors. Vision Res 25, 1795-1810 (1985).

432 9. M. Cynader, N. Berman, Receptive-field organization of monkey superior colliculus. J 433 Neurophysiol 35, 187-201 (1972).

434 10. D. C. Van Essen, W. T. Newsome, J. H. Maunsell, The visual field representation in 435 striate cortex of the macaque monkey: asymmetries, anisotropies, and individual 436 variability. Vision Res 24, 429-448 (1984).

437 11. B. M. Dow, A. Z. Snyder, R. G. Vautin, R. Bauer, Magnification factor and receptive 438 field size in foveal striate cortex of the monkey. Exp Brain Res 44, 213-228 (1981).

439 12. J. E. McGregor et al., Functional architecture of the foveola revealed in the living 440 primate. PLoS One 13, e0207102 (2018).

441 13. Z. M. Hafed, Mechanisms for generating and compensating for the smallest possible 442 saccades. Eur J Neurosci 33, 2101-2113 (2011).

443 14. Z. M. Hafed, C.-Y. Chen, X. Tian, Vision, perception, and attention through the lens of 444 microsaccades: mechanisms and implications. Frontiers in systems neuroscience 9, 167 445 (2015).

446 15. Z. M. Hafed, R. J. Krauzlis, Similarity of superior colliculus involvement in 447 microsaccade and saccade generation. J Neurophysiol 107, 1904-1916 (2012).

448 16. H. K. Ko, M. Poletti, M. Rucci, Microsaccades precisely relocate gaze in a high visual 449 acuity task. Nat Neurosci 13, 1549-1553 (2010).

450 17. Z. M. Hafed, Alteration of visual perception prior to microsaccades. Neuron 77, 775-786 451 (2013).

452 18. A. Cowey, V. H. Perry, The projection of the fovea to the superior colliculus in rhesus 453 monkeys. Neuroscience 5, 53-61 (1980).

454 19. D. H. Hubel, S. LeVay, T. N. Wiesel, Mode of termination of retinotectal fibers in 455 macaque monkey: an autoradiographic study. Brain Res 96, 25-40 (1975).

456 20. V. H. Perry, A. Cowey, Retinal ganglion cells that project to the superior colliculus and 457 pretectum in the macaque monkey. Neuroscience 12, 1125-1137 (1984).

458 21. A. Hendrickson, M. E. Wilson, M. J. Toyne, The distribution of optic nerve fibers in 459 Macaca mulatta. Brain Res 23, 425-427 (1970).

460 22. R. D. Lund, Synaptic patterns in the superficial layers of the superior colliculus of the 461 monkey, Macaca mulatta. Exp Brain Res 15, 194-211 (1972).

462 23. P. H. Schiller, M. Stryker, M. Cynader, N. Berman, Response characteristics of single 463 cells in the monkey superior colliculus following ablation or cooling of visual cortex. J 464 Neurophysiol 37, 181-194 (1974).

465 24. R. H. Wurtz, C. W. Mohler, Enhancement of visual responses in monkey striate cortex 466 and frontal eye fields. Journal of neurophysiology 39, 766-772 (1976).

467 25. P. H. Schiller, The role of the monkey superior colliculus in eye movement and vision. 468 Invest Ophthalmol 11, 451-460 (1972).

469 26. D. P. Munoz, R. H. Wurtz, Fixation cells in monkey superior colliculus. I. Characteristics 470 of cell discharge. J Neurophysiol 70, 559-575 (1993).

471 27. P. H. Schiller, F. Koerner, Discharge characteristics of single units in superior colliculus 472 of the alert rhesus monkey. J Neurophysiol 34, 920-936 (1971).

473 28. M. E. Goldberg, R. H. Wurtz, Activity of superior colliculus in behaving monkey. I. 474 Visual receptive fields of single neurons. J Neurophysiol 35, 542-559 (1972).

475 29. C. Y. Chen, Z. M. Hafed, Orientation and Contrast Tuning Properties and Temporal 476 Flicker Fusion Characteristics of Primate Superior Colliculus Neurons. Front Neural 477 Circuits 12, 58 (2018).

478 30. C. Y. Chen, L. Sonnenberg, S. Weller, T. Witschel, Z. M. Hafed, Spatial frequency 479 sensitivity in macaque midbrain. Nat Commun 9, 2852 (2018).

480 31. Z. M. Hafed, C.-Y. Chen, Sharper, stronger, faster upper visual field representation in 481 primate superior colliculus. Current Biology http://dx.doi.org/10.1016/j.cub.2016.04.059, 482 (2016).

483 32. R. A. Berman, R. H. Wurtz, Exploring the pulvinar path to visual cortex. Prog Brain Res 484 171, 467-473 (2008).

485 33. C. Lee, W. H. Rohrer, D. L. Sparks, Population coding of saccadic eye movements by 486 neurons in the superior colliculus. Nature 332, 357-360 (1988).

487 34. J. Freeman, E. P. Simoncelli, Metamers of the ventral stream. Nat Neurosci 14, 1195- 488 1201 (2011).

489 35. M. Lavidor, V. Walsh, The nature of foveal representation. Nat Rev Neurosci 5, 729-735 490 (2004).

491 36. H. A. Mallot, W. Von Seelen, F. Giannakopoulos, Neural mapping and space-variant 492 image processing. Neural Netw 3, 245-263 (1990).

493 37. F. P. Ottes, J. A. Van Gisbergen, J. J. Eggermont, Visuomotor fields of the superior 494 colliculus: a quantitative model. Vision Res 26, 857-873 (1986).

495 38. A. Grantyn et al., Density gradients of trans-synaptically labeled collicular neurons after 496 injections of rabies virus in the lateral rectus muscle of the rhesus monkey. J Comp 497 Neurol 451, 346-361 (2002).

498 39. P. M. Daniel, D. Whitteridge, The representation of the visual field on the cerebral cortex 499 in monkeys. J Physiol 159, 203-221 (1961).

500 40. R. A. Marino, C. K. Rodgers, R. Levy, D. P. Munoz, Spatial relationships of visuomotor 501 transformations in the superior colliculus map. J Neurophysiol 100, 2564-2576 (2008).

502 41. C. Y. Chen, Z. M. Hafed, Postmicrosaccadic enhancement of slow eye movements. The 503 Journal of neuroscience : the official journal of the Society for Neuroscience 33, 5375- 504 5386 (2013).

505 42. C. Y. Chen, A. Ignashchenkova, P. Thier, Z. M. Hafed, Neuronal Response Gain 506 Enhancement prior to Microsaccades. Curr Biol 25, 2065-2074 (2015).

507 43. C. Y. Chen, Z. M. Hafed, A Neural Locus for Spatial-Frequency Specific Saccadic 508 Suppression in Visual-Motor Neurons of the Primate Superior Colliculus. J 509 Neurophysiol, jn 00911 02016 (2017).

510 44. A. F. Fuchs, D. A. Robinson, A method for measuring horizontal and vertical eye 511 movement chronically in the monkey. J Appl Physiol 21, 1068-1070 (1966).

512 45. S. J. Judge, B. J. Richmond, F. C. Chu, Implantation of magnetic search coils for 513 measurement of eye position: an improved method. Vision Res 20, 535-538 (1980).

514 46. C. Distler, K. P. Hoffmann, Cortical input to the nucleus of the optic tract and dorsal 515 terminal nucleus (NOT-DTN) in macaques: a retrograde tracing study. Cereb Cortex 11, 516 572-580 (2001).

517 47. K. P. Hoffmann, F. Bremmer, A. Thiele, C. Distler, Directional asymmetry of neurons in 518 cortical areas MT and MST projecting to the NOT-DTN in macaques. J Neurophysiol 87, 519 2113-2123 (2002).

520 48. R. B. Illing, Spatial relation of the acetylcholinesterase-rich domain to the visual 521 topography in the feline superior colliculus. Exp Brain Res 73, 589-594 (1988).

522 49. A. M. Seligman, M. J. Karnovsky, H. L. Wasserkrug, J. S. Hanker, Nondroplet 523 ultrastructural demonstration of cytochrome oxidase activity with a polymerizing 524 osmiophilic reagent, diaminobenzidine (DAB). J Cell Biol 38, 1-14 (1968).

525 50. X. Tian, M. Yoshida, Z. M. Hafed, A Microsaccadic Account of Attentional Capture and 526 Inhibition of Return in Posner Cueing. Frontiers in systems neuroscience 10, 23 (2016).

527 51. X. Tian, M. Yoshida, Z. M. Hafed, Dynamics of fixational eye position and 528 microsaccades during spatial cueing: the case of express microsaccades. J Neurophysiol 529 119, 1962-1980 (2018).

530 52. A. Buonocore et al., Alteration of the microsaccadic velocity-amplitude main sequence 531 relationship after visual transients: implications for models of saccade control. J 532 Neurophysiol, jn 00811 02016 (2017).

533 53. C. W. Mohler, R. H. Wurtz, Organization of monkey superior colliculus: intermediate 534 layer cells discharging before eye movements. J Neurophysiol 39, 722-744 (1976).

535 54. H. B. Barlow, C. Blakemore, J. D. Pettigrew, The neural mechanism of binocular depth 536 discrimination. J Physiol 193, 327-342 (1967).

537 55. N. K. Humphrey, Responses to visual stimuli of units in the superior colliculus of rats 538 and monkeys. Exp Neurol 20, 312-340 (1968).

539 56. Z. M. Hafed, L. Goffart, R. J. Krauzlis, A neural mechanism for microsaccade generation 540 in the primate superior colliculus. Science 323, 940-943 (2009).

541 57. R. H. Wurtz, J. E. Albano, Visual-motor function of the primate superior colliculus. Annu 542 Rev Neurosci 3, 189-226 (1980).

543 58. D. P. Munoz, R. H. Wurtz, Saccade-related activity in monkey superior colliculus. I. 544 Characteristics of burst and buildup cells. J Neurophysiol 73, 2313-2333 (1995).

545 59. M. Gur, D. M. Snodderly, High response reliability of neurons in primary visual cortex 546 (V1) of alert, trained monkeys. Cereb Cortex 16, 888-895 (2006).

547 60. Y. Tang et al., Eye position compensation improves estimates of response magnitude and 548 receptive field geometry in alert monkeys. J Neurophysiol 97, 3439-3448 (2007).

549 61. B. Haider, M. Hausser, M. Carandini, Inhibition dominates sensory responses in the 550 awake cortex. Nature 493, 97-100 (2013).

551 62. A. Vaiceliunaite, S. Erisken, F. Franzen, S. Katzner, L. Busse, Spatial integration in 552 mouse primary visual cortex. J Neurophysiol 110, 964-972 (2013).

553 63. C. T., H. J., A dendrite method for cluster analysis. Communications in Statistics - 554 Theory and Methods 3, 1-27 (1974).

555 64. C. R. Legendy, M. Salcman, Bursts and recurrences of bursts in the spike trains of 556 spontaneously active striate cortex neurons. J Neurophysiol 53, 926-939 (1985).

557 65. D. A. Robinson, Eye movements evoked by collicular stimulation in the alert monkey. 558 Vision Res 12, 1795-1808 (1972).

559 66. D. P. Munoz, R. H. Wurtz, Saccade-related activity in monkey superior colliculus. II. 560 Spread of activity during saccades. J Neurophysiol 73, 2334-2348 (1995).

561 67. P. Andrey, Y. Maurin, Free-D: an integrated environment for three-dimensional 562 reconstruction from serial sections. J Neurosci Methods 145, 233-244 (2005).

563 68. E. Calabrese et al., A diffusion tensor MRI atlas of the postmortem rhesus macaque 564 brain. Neuroimage 117, 408-416 (2015).

565 69. P. A. Yushkevich et al., User-guided 3D active contour segmentation of anatomical 566 structures: significantly improved efficiency and reliability. Neuroimage 31, 1116-1128 567 (2006).

568 70. R. H. Wurtz, M. E. Goldberg, Superior colliculus cell responses related to eye 569 movements in awake monkeys. Science 171, 82-84 (1971).

570

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574

575 576 Acknowledgments 577 We are grateful to H. Korbmacher and E. Brockmann for technical support. C.-Y.C. and Z.M.H. 578 were funded by the following sources: (1) Deutsche Forschungsgemeinschaft (DFG, German 579 Research Foundation) – Projektnummer 276693517 – SFB 1233), (2) the Hertie Institute for 580 Clinical Brain Research (HIH), and (3) the Werner Reichardt Centre for Integrative 581 Neuroscience (CIN). The CIN is an excellence cluster funded by the DFG (EXC 307). C.D. and 582 K.-P.H. were funded by DFG grant Ho-450/25-1 and by ZEN grant 1.001/09/013 of the 583 Gemeinnuetzige Hertie Foundation.

584 585 Author contributions 586 C.-Y.C., C.D., K.-P.H., and Z.M.H. designed the study. C.-Y.C. and Z.M.H. conducted the 587 awake monkey experiments. C.D. and K.-P.H. conducted the anesthetized monkey experiments. 588 C.-Y.C., C.D., K.-P.H., and Z.M.H. analyzed the data. Z.M.H. wrote the manuscript. C.-Y.C., 589 C.D., K.-P.H., and Z.M.H. edited the manuscript. 590 591 Competing interests 592 Authors declare no competing interests. 593 594 595 596 597

598 Materials and Methods

599 Animal preparation for the awake monkey experiments (monkeys N and P)

600 Macaque monkeys N and P (male, Macaca mulatta, aged 7 years and weighing 7-10 kg)

601 were prepared earlier (31, 41-43). Briefly, we surgically attached a titanium head holder to each

602 monkey’s skull with titanium skull screws. The head holder was used for stabilizing head

603 position during experiments. After recovery and initial behavioral training, we implanted a

604 scleral search coil in one eye to allow eye movement measurement using the magnetic induction

605 technique (44, 45). For neural recordings from superior colliculus (SC), we implanted recording

606 chambers, placed on the midline with chamber center being aimed at a point 1 mm posterior of

607 and 15 mm above the interaural line (42). The chambers were tilted backward from vertical by

608 35 deg in monkey N and 38 deg in monkey P.

609 All experiments were approved by ethics committees at the regional governmental offices

610 of the city of Tuebingen (Regierungspräsidium Tübingen), and they were in accordance with

611 European Union directives on animal research, along with the German governmental

612 implementations of these directives.

613

614 Animal preparation for the anesthetized monkey experiments (monkeys R and F)

615 Two additional male macaque monkeys (monkey F, Macaca fascicularis, aged 13 years,

616 weighing 6.3 kg; monkey R, Macaca mulatta, aged 6 years, weighing 7 kg) were used. Both

617 monkeys had also taken part in other projects (46, 47). All experiments were approved by the

618 local authorities (Regierungspräsidium Arnsberg, now LANUV) and ethics committee, and they

619 were performed in accordance with the Deutsche Tierschutzgesetz of 7.26.2002, the European

27 bioRxiv preprint doi: https://doi.org/10.1101/554121; this version posted February 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

620 Communities Council Directive RL 2010/63/EC, and NIH guidelines for care and use of animals

621 for experimental procedures.

622 The animals were pre-medicated with 0.04mg/kg atropine and initially anesthetized with

623 10mg/kg ketamine hydrochloride i.m. (Braun, Melsungen, Germany). After local anesthesia with

624 10% xylocain (Astra Zeneka, Wedel), they were intubated through the mouth, and an intravenous

625 catheter was placed into the saphenous vein. After additional local anesthesia of their auditory

626 canals and the skin above the planned craniotomy with bupivacain hydrochloride 0.5%

® ® 627 (Bupivacain , DeltaSelect, Pfullingen, Germany) or prilocainhydrochloride 0.5% (Xylonest ,

628 Astra Zeneca, Wedel, Germany), the animals were placed into a stereotaxic apparatus and

629 artificially ventilated with a nitrous oxide:oxygen ratio of 3:1. Ventilation also contained 0.3-1%

630 halothane as needed according to no change in heart rate during algetic stimuli (1% during

631 surgery, 0.3-0.5% during recording). The skin overlying the skull was cut, and a craniotomy was

632 performed to allow access to the SC, either vertically from above (monkey R) or at an angle of

633 45 deg posterior (monkey F). Heart rate, SPO2, blood pressure, body temperature, and end-tidal

634 CO2 were monitored constantly and maintained at physiological values. Corneae were protected

® 635 with contact lenses chosen with a refractometer (Rodenstock ) to focus the animals’ eyes on the

636 projection screen. After surgery completion, the animals were paralyzed with alcuronium

® 637 chloride (Alloferin , MedaPharma, Germany).

638

639 Histology (monkeys R and F)

640 Monkeys N and P are still being used for experiments. Monkeys R and F were sacrificed to

641 reconstruct a 3-dimensional model of superficial SC surface topography (Figs. 3, 4, S6). At the

642 end of the experiments, the animals received a lethal dose of pentobarbital (80-100mg/kg), and

28 bioRxiv preprint doi: https://doi.org/10.1101/554121; this version posted February 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

643 they were perfused through the heart with 0.9% NaCl with 0.1% procaine hydrochloride

644 followed by paraformaldehyde-lysine-periodate containing 4% paraformaldehyde. After

645 postfixating the tissue overnight, it was cryoprotected with 10% and 20% glycerol in 0.1 molar

646 phosphate buffer (pH 7.4) and then flash frozen in isopentane and stored at -70°C.

647 Frozen sections through midbrain were cut at 40µm in the frontal plane (monkey R) or at

648 50µm in a plane perpendicular to SC surface (monkey F). To visualize recording sites and tracer

649 injections (46), alternate series were used for Nissl stain, acetylcholine esterase (AChE) (48)

650 histochemistry, cytochrome C oxidase histochemistry (49), myeloarchitecture, and tracer

651 protocols (46). The histological sections were photographed by a photomicroscope (Zeiss

652 Axioplan) equipped with a Canon EOS 600D camera. Brightness and contrast were adjusted with

653 Adobe Photoshop (RRID: SciRes_000161, version 5.5).

654

655 Behavioral tasks for the awake monkey experiments (monkeys N and P)

656 The animals were trained to maintain precise gaze fixation on a small spot measuring

657 8.5x8.5 min arc (41). The same animals were extensively trained on precise fixation and were

658 used in previous studies demonstrating their high oculomotor control capabilities (41, 43, 50-52).

2 2 659 The fixation spot was a white square (72 Cd/m ) presented over a gray background (21 Cd/m )

660 (31, 42). Within a given recording session, we isolated individual neurons online and

661 characterized them using a variety of behavioral tasks. If the monkey was still interested in

662 continuing after a neuron was recorded, we moved the recording electrode deeper into the SC

663 and isolated additional neurons (e.g. Fig. S4). We recorded between 1 and 6 neurons per session.

664 The behavioral tasks were chosen in part to classify neuron types and in part to characterize

665 foveal visual neuron response properties as in the main text.

29 bioRxiv preprint doi: https://doi.org/10.1101/554121; this version posted February 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

666 Memory-guided saccade task. This task was used to assist in classifying neurons as

667 possessing a saccade-related movement response independent of visual stimulation (53) (see

668 Neuron classification below). A fixation spot was presented for 300-1000 ms. After the monkey

669 established gaze fixation, a second spot was flashed for ~50 ms and disappeared. The monkey

670 had to maintain fixation and remember the flash location. The fixation spot was then removed

671 after 300-1100 ms; the monkey was trained to generate a saccade to the memorized flash

672 location, and then hold gaze at that location (to within a tolerance window dependent on flash

673 eccentricity) for ~300-500 ms before being rewarded. Liquid reward was given if all trial epochs

674 were successfully completed. Flash location was chosen to be at the response field (RF) hotspot

675 of the isolated neuron, which we estimated from the other visual and saccade tasks described

676 below. We collected >35 trials from each neuron. If the neuron elicited a saccade-related

677 response, it was classified as being a movement-related neuron that was independent of visual

678 stimulation (53) (see Neuron classification below).

679 Delayed visually-guided saccade task. This task was used to map visual and saccade-related

680 RF’s. A fixation spot was presented for 300-1000 ms. After the monkey established fixation, a

681 second spot (target) was presented. When the fixation spot was removed 500-1000 ms later, the

682 monkey made a saccade to the target. We varied target location from trial to trial in order to map

683 each neuron’s visual and saccade-related RF’s. For each neuron, we collected 88 +/- 34 s.d.

684 trials. We collected data from 332 neurons in this task. Some of these neurons (mostly the

685 peripheral ones) were used in earlier studies for other purposes (29-31), and they were important

686 here as a suitable reference for comparing, in the same animals, foveal neural response

687 properties.

30 bioRxiv preprint doi: https://doi.org/10.1101/554121; this version posted February 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

688 Fixation visual RF mapping task. For the most foveal neurons, we simplified the delayed

689 visually-guided saccade task. A fixation spot was first presented for 300 -1000 ms. After the

690 monkey established fixation, a second spot was then presented for 250 ms while the monkey

691 maintained fixation. Reward was only contingent on maintaining gaze position at the fixation

692 spot until trial end. We used this task instead of the delayed visually-guided saccade task if the

693 neuron’s RF was too close to the fixation spot, making it difficult to instruct a delayed saccade

694 task. Because microsaccades were inevitable in this task, this task still allowed us to explore

695 saccade-related movement fields as well as visual RF’s, so the task was conceptually comparable

696 to the delayed visually-guided saccade task. For each isolated neuron, we collected 122 +/- 87

697 s.d. trials. We collected data from 81 neurons in this task.

698

699 Visual stimulation in the anesthetized monkey experiments (monkeys R and F)

700 We used small spots of light moved across the screen using a hand-held lamp or laser

701 pointer. Single and multi-unit activity was recorded from the SC surface (upper superficial

702 layer), and RF location and extent were determined by moving the stimulus in various directions

703 and at various speeds across a tangent screen at a distance from the eye of 285 cm for peripheral

704 RF’s and 570 cm for foveal RF’s. To ensure that paralysis was maintained during the

705 experiment, a recording electrode was inserted into the visual cortex (V1) and the RF determined

706 and checked at regular intervals during the entire recording session (also see below for RF area

707 calculations). Horizontal RF borders were determined by moving the stimulus up and down

708 starting outside the RF and then shifting it towards RF center. The same procedure, similar to the

709 minimal response field method of (54), was also used for determining the vertical borders (this

710 time with horizontal stimulus movements).

31 bioRxiv preprint doi: https://doi.org/10.1101/554121; this version posted February 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

711 The exact locations of the horizontal and vertical receptive field borders in deg of visual

712 angle with respect to the eye contralateral to the recorded SC were measured by use of a laser

713 pointer attached to a 2D angle meter. Two calibrated rotary potentiometers aligned with the

714 position where the eye had been during recording allowed direct reading of the azimuth and

715 elevation values in deg.

716

717 Neuron classification

718 For the anesthetized monkeys R and F, we recorded only the most superficial SC neurons.

719 These are purely visual (27, 55), also receiving direct retinal projections (3-5). Therefore, no

720 further classification was done. Neurons encountered at the rostro-lateral border of the SC were

721 assigned to the nucleus of the optic tract if they responded in a direction-selective manner to

722 temporo-nasal movement of large area random dot stimuli. Neurons at the caudal border of the

723 SC were localized in the inferior colliculus if they responded to auditory stimuli (hand clapping,

724 whistling, or clicks).

725 For the awake monkeys N and P, we classified neurons as being purely visual, visual-motor

726 (saccade-related), or purely motor (saccade-related) (31, 42). We classified a neuron as being

727 visually responsive if average neural activity 0-200 ms after target onset in the delayed visually

728 guided-saccade task or the fixation visual RF mapping task was higher than average neural

729 activity 0-200 ms before target onset (baseline activity) (p<0.05, paired t-test.) (31, 42). We also

730 classified a neuron as being motor responsive if average neural activity 0-50 ms before saccade

731 onset in the delayed visually-guided saccade task or the memory-guided saccade task was higher

732 than average neural activity 100-175 ms before saccade (31, 42).

32 bioRxiv preprint doi: https://doi.org/10.1101/554121; this version posted February 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

733 For some neurons, because the RF of the neuron was very close to fixation, the saccadic

734 tasks were deemed at times to be too demanding for the monkeys. In these cases, we collected

735 microsaccades after fixation spot onset but before the second spot onset from fixation visual RF

736 mapping task. We classified the neurons as being motor responsive by applying the same

737 measurement intervals above but now aligned to contraversive microsaccade onset.

738 In total, we analyzed data from 413 neurons from both the right and left SC (162 purely

739 visual, 239 both visually and motor responsive, and 12 purely motor). We often combined purely

740 visual and visual-motor neurons (401 neurons) when analyzing visual response properties, unless

741 a specific difference was noted (e.g. Fig. S2C). We were least interested in purely motor neurons

742 because this was not the focus in our study. Microsaccade-related responses were previously

743 described in the SC (15, 56), and we used motor neurons in the present study to confirm

744 expected vertical organization of visual, visual-motor, and purely motor neurons across the

745 depths of the SC (57, 58) (e.g. Fig. S4).

746

747 Visual and motor-related RF hotspot and area calculations

748 Because foveal RF’s are extremely small (e.g. Fig. 1), even the smallest fixational eye

749 movements can smear stimulus position on the retina and therefore alter estimates of RF hotspot

750 location and area (59, 60). We therefore carefully accounted for eye movement measurements in

751 all of our experiments.

752 For the anesthetized animals (monkeys R and F), we used a reference electrode placed in

753 the foveal representation of the primary visual cortex (V1) to ensure that there were no eye

754 movements during stimulus presentation for the SC experiments; we ensured that the foveal V1

755 neuron was regularly stimulated (visually) after we mapped SC RF’s. Because we analyzed the

33 bioRxiv preprint doi: https://doi.org/10.1101/554121; this version posted February 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

756 entire SC surface topography estimation in a given monkey during a single session with many

757 successive penetrations, we were severely limited in time. We therefore estimated SC RF area by

758 listening to single or multi-unit activity, and we plotted the RF assuming a rectangular shape

759 (e.g. inset in Fig. S3) (54). We demarcated the inner and outer RF locations both horizontally and

760 vertically. Because anesthesia potentially alters RF sizes and neural response properties (61, 62),

761 and because our RF area estimates under anesthesia were less quantitative than the awake

762 monkey procedures described below, we did not perform quantitative comparisons between RF

763 areas in the anesthetized and awake animals. However, we did confirm the same non-uniform

764 sampling of visual space even within the foveola in both anesthetized and awake animals (e.g.

765 Figs. 2A, S3).

766 For the awake monkeys (N and P), we first calibrated eye tracker measurements similar to

767 how we calibrate them in our laboratory (and in the same animals) for our real-time gaze-

768 contingent stimulus presentation experiments (41, 50, 51). We then corrected for a small

769 technical artifact in the magnetic induction eye coil system that happened in a minority of our

770 sessions. Specifically, for a typical ~6-hour recording session, we sometimes observed a small,

771 abrupt jump in eye position using the eye coil system midway through a session. We confirmed

772 that this was a measurement artifact and not a genuine shift in the monkeys’ eye position by

773 performing eye movement analyses (e.g. Fig. 5) and also by comparing our strong RF skewness

774 effects (e.g. Fig. 2B) with and without artifact correction. For monkey N, we also investigated

775 this artifact in more detail by measuring eye position using both a video-based eye tracker

776 (EyeLink 1000, SR Research, Toronto, Canada) and the magnetic induction eye coil system

777 simultaneously (41). We corrected this artifact using the following procedure. We measured

778 average eye position 0-50 ms before stimulus onset in a given task in which a potential artifact

34 bioRxiv preprint doi: https://doi.org/10.1101/554121; this version posted February 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

779 was suspected (i.e. at the end of the initial fixation interval while the monkeys maintained stable

780 fixation). We excluded trials with microsaccade within 0-100 ms before stimulus onset. We then

781 used a Calinski-Harabasz criterion (63) on horizontal eye position, vertical eye position, and trial

782 sequence to find an optimal clustering number, and we then ran a k-means clustering algorithm

783 using the optimal clustering number. We validated the result by manually observing all

784 clustering results. From among all neurons, 300 contained only 1 cluster (no artifact), and 89

785 contained 2 clusters. Only 24 neurons had 3 or more clusters. For the multi-cluster files, we

786 corrected the artifact by shifting the displaced clusters to the centroid of the main eye position

787 cloud.

788 With technical calibration now corrected, we were now in a position to estimate RF

789 properties. For estimating the visual RF area, we excluded all trials containing microsaccades

790 within +/-100 ms around stimulus onset time. We then measured peak firing rate 30-150 ms after

791 stimulus onset. We related this visual response property to retinotopic stimulus location in order

792 to estimate RF area in retinotopic coordinates. We obtained retinotopic stimulus location by

793 accounting for fixational eye position variation across time and trials (50, 51). Specifically, we

794 measured average eye position 0-50 ms before stimulus onset and related it to the calibrated eye

795 position. We then shifted the true stimulus location in physical display coordinates to the

796 retinotopic location relative to the center of gaze. For example, if the stimulus was physically

797 presented at 15 min arc to the right of the fixation spot on the display, but the eye position at

798 stimulus onset was shifted by 5 min arc to the left of calibrated eye position, then the true

799 stimulus location in retinotopic coordinates was in reality at 20 min arc to the right of the center

800 of gaze. Across all stimulus locations and peak firing rate measurements, we used Delaunay

801 triangulation and linearly interpolated the firing rate measurements to obtain a 3-dimensional

35 bioRxiv preprint doi: https://doi.org/10.1101/554121; this version posted February 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

802 surface of visual response strength as a function of 2-dimensional stimulus location. We further

803 applied a threshold to accept a location as being within a given RF. The threshold was that the

804 visual response had to be >3 s.d. above baseline pre-stimulus firing rate during fixation. All

805 locations with visual responses above this threshold were considered to be within the visual RF

806 of a given neuron, and RF hotspot location was the location eliciting the strongest visual

807 response. This procedure gave us a more accurate estimate of the RF area and shape, especially

808 when the neurons were extremely close to the fovea (e.g. Fig. 2B, left panel), and we confirmed

809 that eye position correction resulted in smaller RF’s than without correction (59, 60). For

810 example, across all neurons (including eccentric ones), the average RF area decreased by 4.2

811 percent after correction for eye movements.

812 We used a similar procedure to estimate saccade-related motor RF’s. In this case, we

813 measured average firing rate 0-50 ms before saccade onset, and we used saccadic horizontal and

814 vertical eye position deviations as the locations against which we plotted saccade-related firing

815 rate.

816 In summary analyses (e.g. Figs. 2A, S3A, S5), we binned eccentricities into 0.25 deg bin

817 widths and used a running window of 0.5 deg step size. In Fig. 4B, for visualizing a larger

818 eccentricity range, we used 0.5 deg bin widths and a running window of 1.5 deg step size.

819

820 Visual RF skewness

821 To estimate visual RF skewness along radial retinotopic eccentricity (e.g. Fig. 2B, C), we

822 plotted a 1-dimensional RF profile: we plotted visual response strength as a function of radial

823 retinotopic eccentricity along the line connecting the center of gaze to the RF hotspot. To

824 compare neurons, we normalized each neuron’s 1-dimensional RF profile along eccentricity by

36 bioRxiv preprint doi: https://doi.org/10.1101/554121; this version posted February 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

825 the neuron’s response at the peak hotspot location. We then combined neurons having a similar

826 preferred retinotopic eccentricities (e.g. Fig. 2B). For population statistics of skewness, we fit

827 each neuron’s 1-dimensional RF profile as a function of radial eccentricity to a beta function, and

828 we acquired the a and b parameters of the fit. These allowed us to estimate the near and far

829 ratios (a-to-b ratios in Fig. 2C) of the RF. We reasoned that this approach of fitting was a more

830 unbiased method for evaluating RF skewness because the mapping could sometimes be

831 incomplete close to the far edge of the RF; fitting takes into account the entire measurement for

832 estimating a-to-b ratios. We also felt that the fitting gives a direct quantitative measure of RF

833 skewness, but the skewness is also very evident in raw traces as well (Fig. 2B).

834 To further evaluate the above method, for the same neurons included in the current analysis,

835 we also took another 1-dimensional RF profile, but this time as a function of direction from

836 horizontal along the radial eccentricity of the RF hotspot (e.g. c-to-d ratio in Fig. 2C). The

837 prediction would be that the ratio of the a and b parameters in the beta function fit would now be

838 close to 1 because the asymmetry that we observed in RF’s was only observed along the radial

839 dimension (Fig. 2B, C). In Fig. 2C, all neurons with preferred visual eccentricity <2 deg were

840 analyzed, except for 6 neurons. These neurons were excluded because the RF data fit to a beta

841 function did not result in >80% explained variance by the fit.

842

843 Visual response sensitivity and latency

844 In Fig. S2B, we used the highest visual response within a neuron’s RF (i.e. at the RF

845 hotspot) as the preferred eccentricity of each neuron. We then binned eccentricities into 0.25 deg

846 bin widths, and we used a running window of 0.5 deg step size, to plot visual sensitivity as a

847 function of preferred eccentricity. We combined neurons from different depths below SC surface

37 bioRxiv preprint doi: https://doi.org/10.1101/554121; this version posted February 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

848 because we did not find any significant difference in SC visual response sensitivity across depth

849 from the SC surface. For example, comparing visual sensitivity of neurons with <1000 µm depth

850 below SC surface to visual sensitivity of neurons with 1000-2000 µm depth resulted in a non-

851 significant effect (Ranksum test, p=0.90848, all neurons preferring <2 deg eccentricity).

852 To estimate a neuron’s response latency, we first applied Poisson spike train analysis to find

853 the first spike occurring in response to stimulus onset for each trial (29-31, 64). This method was

854 particularly suitable when a neuron had an ongoing baseline firing rate on which a stimulus-

855 evoked response rode; the method also trivially detected first-spike latency when there was no

856 baseline rate before stimulus onset (e.g. Neurons #1-#4 in Fig. 1). To ensure that we were

857 estimating first-spike latency for optimal stimuli across neurons, we estimated each neuron’s

858 response latency by averaging first-spike latency only from trials in which the stimulus was near

859 the RF hotspot (i.e. evoking a response larger than half of the peak visual response within a

860 neuron’s RF; typically >22 trials). After we estimated each neuron’s response latency for the

861 optimal stimulus location, we plotted the response latency across neural preferred eccentricity

862 using 0.25 deg bin widths and a running window step size of 1 deg. We separated superficial

863 (<1000 µm below SC surface) and deeper (1000-2000 µm below SC surface) neurons in this

864 analysis because we observed a difference in how response latency depended on eccentricity

865 within foveal space (< 2 deg) as a function of neural depth below SC surface (Fig. S2C).

866

867 Neural modulations during ocular drift fixational eye movements

868 To demonstrate that tiny fixational eye movements can have a significant influence on

869 neural variability in the foveal representation, even when no stimuli are presented on the display

870 except for a fixation spot, we identified neurons having a baseline firing rate during fixation (Fig.

38 bioRxiv preprint doi: https://doi.org/10.1101/554121; this version posted February 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

871 5). We further only considered trials in which there were no microsaccades for at least 100 ms

872 before stimulus onset (i.e. at the end of the baseline fixation period). In these trials, the only

873 stimulus on the display was the fixation spot (Fig. 5A); our goal was to investigate whether drifts

874 of the image of the fixation spot into and out of a foveal neuron’s visual RF (because of

875 fixational eye movements) would be sensed by the neurons.

876 We analyzed eye movements along the axis connecting the center of gaze to the RF hotspot

877 location; that is, we rotated the eye position and RF data based on each neuron’s RF hotspot

878 location such that the RF hotspot in the new coordinate reference frame was always to the right

879 of the center of gaze (Fig. 5A). This allowed us to investigate eye position variation to or away

880 from the RF (because after rotation, the horizontal eye position change was going to move the

881 fixation spot in or out of the RF, the vertical eye position component was orthogonal to the RF

882 and was less relevant for this analysis; we therefore excluded it from analysis for simplicity).

883 Next, we filtered our neurons to those having RF hotspot locations being <1 deg in

884 eccentricity and also firing >50 spikes in the final 100 ms before stimulus onset. The latter

885 criterion allowed us to have a more sensitive analysis for this particular question that we were

886 interested in addressing. We also excluded neurons with microsaccades in the critical analysis

887 period. This resulted in 27 neurons for this analysis.

888 Across trials, we sorted microsaccade-free eye positions based on whether they brought the

889 fixation spot towards the RF border (Fig. 5B, top, “Away” eye positions) or away from it. If the

890 neuron was sensitive to the influence of ocular drift on retinal images, then more action

891 potentials should be triggered whenever the image of the fixation spot was brought towards the

892 RF location (Fig. 5B, C, top). To plot spike-aligned eye position (Fig. 5B, C, bottom), we took

893 every neural action potential (spike) in the final 100 ms of fixation before stimulus onset, and we

39 bioRxiv preprint doi: https://doi.org/10.1101/554121; this version posted February 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

894 plotted the average eye position (along the RF axis) leading up to this action potential. We then

895 averaged all spike-aligned eye positions. Relatively speaking, more eccentric neurons should

896 require larger eye position variation to trigger response variability than less eccentric neurons

897 (e.g. Neurons #6 and #5, respectively, in Fig. 5B, C).

898

899 Shifts in foveal visual RF hotspot locations prior to microsaccades

900 To analyze the impacts of the second type of fixational eye movement that can take place

901 (microsaccades) on foveal visual representations in the SC, we searched for neurons in our

902 database having sufficient numbers of trials satisfying the following criteria. First, stimulus onset

903 had to occur before microsaccades (within 100 ms), such that we can analyze evoked responses

904 even before a shift in eye position had taken place. Second, there had to be sufficient trials to

905 allow estimating a map of the RF (>10 trials within the RF region). Third, the microsaccades had

906 to be directed opposite the hemifield represented by the SC side that we were recording from, so

907 that we could avoid observing microsaccade-related elevations in firing rate (56), which can

908 mask visually-evoked responses by stimulus onset. Fourth, the neurons had to show no

909 microsaccade-related movement burst for these ipsiversive microsaccades. Finally, the neurons

910 had to have RF hotspot locations <2 deg in eccentricity. We then reconstructed visual RF maps

911 without microsaccades (as in all of our analyses) or when stimuli appeared in pre-microsaccadic

912 intervals. Since these intervals are associated with perceptual mislocalizations in the fovea (17),

913 we analyzed whether RF hotspot locations were shifted by amounts larger than predicted by

914 simple shifts in eye position caused by the microsaccades themselves. Because all of our

915 calibrations in eye position were done for microsaccade-free fixation (see Visual and motor-

916 related RF hotspot and area calculations above), we also confirmed that eye position shifts

40 bioRxiv preprint doi: https://doi.org/10.1101/554121; this version posted February 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

917 caused by microsaccades in the present analysis were insufficient to explain our results (e.g. Fig.

918 6B). We included 24 neurons in this analysis; on average, we had 22 +/- 15.3 s.d. trials for each

919 neuron with microsaccades.

920

921 Estimating a new SC surface topography map from (37)

922 The universally accepted map of SC topography (37) was based on peripheral

923 measurements of electrically-evoked saccades from (65). We used a similar approach to (65), but

924 now densely mapping the most superficial SC laminae in monkeys R and F and with visual

925 stimuli as opposed to electrical microstimulation of the deeper saccade-related layers. We also

926 made sure to measure both peripheral and foveal sites.

927 We mapped the left SC of monkey F using 500 µm resolution, and using a penetration angle

928 tilted 45 deg posterior of vertical. In monkey R, we mapped the right SC surface topography

929 using 250 µm resolution and vertical penetrations. During the mappings, we also physiologically

930 determined the SC borders, by identifying neighboring sites (Fig. S6A). We performed 91

931 penetrations, ranging from 0.1 to 49 deg in eccentricity in monkey F, and 124 penetrations,

932 ranging from 0.04 to 12 deg in monkey R. In order to align the SC from the two monkeys, and to

933 obtain a direct comparison to (37), we projected monkey R’s recordings into the same 45 deg

934 posterior of vertical coordinate frame (like monkey F). We did this because the original

935 peripheral SC mappings (65), based on which the universally accepted SC topography map (37)

936 was obtained, were performed using the same approach.

937 We then ran a rigid body transformation to align recording sites from the two monkeys. In

938 the visual region of overlap between the two monkeys (up to 12 deg eccentricity), we minimized

939 the least-mean-square error between the preferred eccentricity and visual angles of SC sites from

41 bioRxiv preprint doi: https://doi.org/10.1101/554121; this version posted February 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

940 the two monkeys. This allowed co-registration of the two SC’s. We validated this co-registration

941 by plotting the non-SC locations that we physiologically measured during the experiments. We

942 confirmed that none of the non-SC sites after co-registration encroached on our aligned SC sites.

943 We also confirmed that there was good agreement in the non-SC sites with known anatomical

944 geometry relative to SC location (e.g. pretectum or cerebellum), and that our map was even

945 consistent with 3-dimensional anatomy of the SC (see Reconstruction of 3-dimensional SC

946 anatomy below). The results of the final co-registration are shown in Fig. S6A.

947 After co-registration, we checked whether foveal sites have organized topography or not,

948 and in a continuous manner with peripheral representation. We identified sites having 0.5 deg

949 preferred visual eccentricity in their visual responses, and we then interpolated between these

950 sites to draw a 0.5-deg iso-eccentricity line. We repeated this procedure for 1, 2, 5, 10, 20, and

951 40 deg eccentricities (Fig. 3A). We similarly checked iso-direction lines (Fig. 3B).

952 Finally, to obtain a mathematical fit (37), we repeated a procedure similar to that in (37).

953 Critically, the key element here was that we had measurements from both foveal and peripheral

954 sites, unlike in (37, 65). We first rotated the co-registered sites to make the interpolated

955 horizontal meridian (i.e. 0 deg direction line) lie along a horizontal line (e.g. Fig. 3A-D with

956 anatomically-accurate orientation of the horizontal meridian representation versus Fig. 4A with a

957 rotated map to align the horizontal meridian along a horizontal plotting line). We then ran the

958 equations of (37), which are:

⎛ R2 + 2ARcos(θ)+ A2 ⎞ 959 X B log ⎜ ⎟ (Equation 1) = x e ⎜ ⎟ ⎝ A ⎠

⎛ Rsin(θ) ⎞ 960 Y = By arctan⎜ ⎟ (Equation 2) ⎝ Rcos(θ)+ A ⎠

42 bioRxiv preprint doi: https://doi.org/10.1101/554121; this version posted February 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

961 where X and Y are anatomical distances along the SC axis (X being along the axis of the

962 horizontal meridian and Y being the axis along the orthogonal axis of directions from horizontal),

963 R and q are visual coordinates in eccentricity (R) and direction from horizontal (q), and Bx, By,

964 and A are model parameters. For a given R and q in visual coordinates, X and Y specify the

965 corresponding locations in SC tissue coordinates. We obtained new model parameters for the

966 above equations by minimizing the least-mean-square error from the equations to our data

967 similarly to the original paper method. Critically, we used all of our measurements for the data fit

968 and not just the iso-eccentricity and iso-direction. We further verified the result by plotting the

969 new parameters on top of our data to visualize the origin of the SC, and we confirmed that the

970 origin was not in the non-SC regions from our dense mappings. The result is shown in Fig. 3C.

971 We also confirmed that our results provide a much better fit than the original model in (37) (Fig.

972 3D). The new model parameters were 1.1 (Bx), 1.8 (By), and 0.9 (A).

973 To estimate the size of the active population of neurons in SC tissue for a given visual

974 stimulus location, transformation of RF shapes from visual coordinates into SC tissue

975 coordinates is needed (31, 37, 40, 66). Once this transformation is done, it is trivial to estimate

976 the size of the active population for a given stimulus location: this is achieved by simply

977 checking which neurons in the SC map would be activated by the stimulus (and to what extent

978 according to the stimulus location relative to the RF hotspot location) based on the relative

979 positioning between stimulus location and RF coordinates in neural tissue space (31, 37, 40, 66).

980 We thus converted visual RF’s into SC tissue coordinates (Fig. 4A). To do this, we simply

981 plotted firing rate maps as a function of position in the SC tissue space as opposed to visual

982 location. In other words, for every visual location at which we measured RF responses, we

43 bioRxiv preprint doi: https://doi.org/10.1101/554121; this version posted February 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

983 converted its eccentricity and direction pair (R, q) from Equations 1 and 2 above into neural

984 tissue coordinates X and Y.

985

986 Foveal tissue magnification factors

987 In Fig. 3E, we computed linear foveal magnification factor (mm of neural tissue in the

988 SC map per deg of visual angle in visual space) along the horizontal meridian. We did this for

989 the original universally accepted model of SC topography (37) as well as for our new model. We

990 densely sampled the horizontal meridian representation in both models using 0.1 deg visual

991 eccentricity resolution, and we plotted the difference of tissue distance from one sample to the

992 next (appropriately dividing by the step in eccentricity to obtain a correct mm/deg measure).

993 In Fig. 3F, we wanted to compare the linear foveal magnification factor in the SC to that

994 in the primary visual cortex (V1). However, a direct quantitative comparison of V1 foveal

995 magnification factor to Fig. 3E would have been inappropriate and unfair because the SC is

996 approximately an order of magnitude smaller in size than V1. Therefore, we first scaled the SC

997 size upwards in order to match the size of V1, and we then compared quantitative measures. We

998 scaled the SC upwards based on quantitative measures of V1 size. Specifically, we multiplied SC

999 distance along the horizontal meridian by a scale factor that was based on the ratio of linear

1000 distances from 2.5 deg eccentricity to 40 deg eccentricity in both the SC and V1. In the SC, the

1001 distance (between 2.5 deg and 40 deg eccentricity lines) from our measurements was 2.8463

1002 mm. In V1, we estimated this distance to be 25.2014 mm based on (10). Therefore, we scaled the

1003 SC’s horizontal meridian representation by a factor of 8.8541 (equal to 25.2014/2.8463) before

1004 comparing SC foveal tissue magnification to that in V1. The comparison was then done by

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1005 plotting our scaled estimate of SC foveal tissue magnification (if the SC was of approximately

1006 the same physical size as V1) to V1 data reported in (11) from multiple studies (Fig. 3F).

1007

1008 Reconstruction of 3-dimensional SC surface anatomy and alignment with normalized

1009 postmortem MRI’s

1010 We used dense mappings in monkeys R and F and histological sections to develop a

1011 detailed 3-dimensional characterization of macaque SC surface topography. To register the

1012 physiological recordings to a common MRI space, we needed an intermediate step to align the

1013 anatomical locations of the recordings. In one penetration, we therefore made an electrolytic

1014 lesion close to the SC (monkey R; Fig. S6A). We took all histological sections containing SC,

1015 and we manually traced the SC border (Fig. S6B). We next interpolated the outline of the SC in

1016 3-dimensions using Free-D (67) (Fig. S6B), and we used rigid body transformation to register the

1017 reconstructed 3-dimensional SC to a published normalized MRI common space for postmortem

1018 macaque monkeys (68) (Fig. S6C). We used the cerebral aqueduct as our landmark and for

1019 registration with the standard MRI image. After the registration, we used the electrolytic lesion

1020 mark from monkey R to register the physiological recordings to the MRI. We also plotted the SC

1021 and non-SC regions (as identified physiologically) to confirm that our registration procedure

1022 matched with the known anatomical landmarks on the MRI image (Fig. S6D; Movie S1).

1023 Finally, we rendered the MRI data with ITK-SNAP (69) and plotted our new parameters on the

1024 rendered image (Fig. S6E; Movie S2). Data Table S1 contains 3-dimensional coordinates of right

1025 SC surface iso-eccentricity and iso-direction lines in our new model of SC topography.

1026

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1027

1028

1029

1030 1031 Figure S1 Sampled foveal locations represented by SC neurons in all of our four monkeys. (A) The left panel shows 1032 preferred RF hotspot locations identified in awake monkeys N and P, and the right panel shows preferred RF hotspot 1033 locations identified in anesthetized monkeys R and F. The neurons are color-coded according to their preferred hotspot 1034 eccentricity. We sampled a substantial number of neurons representing a region of visual space within the rod-sparse 1035 foveola area of the retinal image (<0.5 deg preferred eccentricity). (B) The same data as in A along with additional 1036 neurons (1-2 deg preferred eccentricity), demonstrating approximately uniform sampling of all possible eccentricities 1037 <2 deg. More eccentric neurons (>2 deg) are not shown, but they were included in all of our analyses for critical 1038 comparisons to foveal SC representations. Note that we recorded in both right and left SC’s in each of monkeys N and 1039 P, but we rotated all neurons into one visual hemifield for figure simplicity. All neurons had visual RF hotspots that 1040 were located in the contralateral visual hemifield to the recorded SC. For monkeys R and F, we recorded from right 1041 SC (representing the left visual hemifield) in monkey R and left SC (representing the right visual hemifield) in monkey 1042 F, but we again rotated the data in this figure for presentation purposes. 1043

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1044

1045

1046 1047 Figure S2 Visual properties of foveal SC neurons. (A) Most neurons in the awake animals, whether foveal (solid line) 1048 or eccentric (dashed line), had little baseline activity. For each neuron, we measured average firing rate within a 200- 1049 ms baseline interval in monkeys N and P (Materials and Methods). (B) For all neurons with preferred eccentricity <2 1050 deg (Fig. S1, awake monkeys N and P), we plotted peak visual response near the preferred RF hotspot location 1051 (Materials and Methods) as a function of preferred eccentricity. For comparison, we also plotted visual response 1052 sensitivity for neurons preferring 8-10 deg eccentricities (again with stimuli appearing at the respective RF hotspots). 1053 SC foveal visual sensitivity was as strong as that at 8-10 deg (Ranksum test, p= 0.63753). Also, within the central 2 1054 deg, there was no dependence of visual sensitivity on neuronal preferred eccentricity (1-way ANOVA, F=0.1924, 1055 p=0.9014). (C) We measured the latency to first stimulus-evoked action potential (spike) for the same locations and 1056 neurons as in B. In this case, we separated the neurons as being either superficial (<1000 µm below SC surface) or 1057 deeper (1000-2000 µm below SC surface) because they showed different results. Superficial neurons (blue), which 1058 are retina-recipient (3-5), had longer first-spike visual response latencies within the foveola region and decreased their 1059 response latency with increasing eccentricity in the rest of the central 2 deg (1-way ANOVA, F=3.4096, p=0.023). 1060 This might reflect an impact of rod-sparse foveolar cone input to neurons (whether directly or through cortex) 1061 representing <0.5 deg eccentricities. Deeper neurons (red), not receiving direct retinal input, did not show a 1062 dependence of first-spike latency on eccentricity in the central 2 deg (1-way ANOVA, F=0.7479, p=0.5288). Note 1063 also that superficial neurons responded earlier than deeper neurons in general (Ranksum test, p=0.0040, all 1064 eccentricities <2 deg; p=6.375x10-6, all eccentricities), consistent with peripheral results (30). Error bars denote s.e.m. 1065

47 bioRxiv preprint doi: https://doi.org/10.1101/554121; this version posted February 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

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1068 1069 Figure S3 Non-uniform sampling within the SC foveal visual representation even in anesthetized monkeys. (A) For 1070 monkeys R and F, we performed similar analyses on visual RF area to those presented in Fig. 2A for the awake 1071 monkeys. The inset shows how we assessed RF area in these anesthetized cases (Materials and Methods). Error bars 1072 denote s.e.m. (p=0.05, 1-way ANOVA as a function of eccentricity, F=2.75, n=66). (B) Data from the central 2 deg 1073 are now shown along with the rest of the neurons that we sampled. Each dot represents a single neuron (as in Fig. 2A), 1074 and we now plot data on a logarithmic scale because of the large range of eccentricities and areas that we measured. 1075 The blue line shows a linear regression fit of all data points (on the logarithmically transformed scales). Like with the 1076 awake monkeys (Fig. 2A), the SC foveal visual representation formed a continuum, in terms of spatial sampling 1077 resolution, with the peripheral representation, showing a supra-linear growth in RF area as a function of increasing 1078 eccentricity. The dashed vertical line delineates the 2 deg eccentricity line. Foveal neurons (<2 deg preferred 1079 eccentricity) clearly showed non-uniform sampling resolution, like in the peripheral representation, and also like in 1080 the awake animals (Fig. 2A). Note that we did not quantitatively compare RF areas between awake and anesthetized 1081 animals due to several experimental constraints (Materials and Methods). 1082

48 bioRxiv preprint doi: https://doi.org/10.1101/554121; this version posted February 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

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1085 1086 Figure S4 Consistent vertical organization of visual and visual-motor neurons within the SC foveal representation. 1087 (A) Example visual RF maps from 5 different neurons isolated within the same recording session in an awake monkey, 1088 as the recording electrode was advanced deeper and deeper into the SC (Materials and Methods). Each plane along 1089 the z-axis plots a pseudocolor surface describing peak visual response after stimulus onset (color-coded) as a function 1090 of horizontal and vertical target eccentricity (x- and y-axes). The z-axis plane at which each surface is drawn indicates 1091 the depth at which the neuron was encountered relative to SC surface. As can be seen, neurons within a single “depth 1092 column” of the SC had similar preferred eccentricities, consistent with peripheral SC representations. (B) The three 1093 deepest neurons from A also had microsaccade-related movement RF’s (Materials and Methods) (15, 56). Thus, the 1094 most superficial two neurons were purely visual neurons (no movement-related discharge), whereas the deeper three 1095 neurons were visual-motor neurons. This ordering of visual and visual-motor neurons is consistent with peripheral SC 1096 depth-related organization (70). 1097

49 bioRxiv preprint doi: https://doi.org/10.1101/554121; this version posted February 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

1098

1099 1100 Figure S5 Non-uniform spatial sampling within the SC representation of foveal space even for movement-related 1101 RF’s. For the awake monkeys N and P, we measured microsaccade- and saccade-related responses (Materials and 1102 Methods), and we performed the same RF area analyses on these responses. Within the foveal representation, we 1103 observed similar non-uniform sampling resolution, in terms of RF area, that we observed for visual RF’s (e.g. compare 1104 to Fig. 2A and Fig. S3) (p=1.260x10-3, 1-way ANOVA as a function of eccentricity, F=6.05, n=58). Note that 1105 microsaccade-related movement RF’s in the fovea (<1 deg) were substantially smaller than visual RF’s in the same 1106 animals (Ranksum test, p=2.180x10-5) (15, 56). Error bars denote s.e.m. 1107

50 bioRxiv preprint doi: https://doi.org/10.1101/554121; this version posted February 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

1108

1109 1110 Figure S6 Reconstruction of 3-dimensional SC surface anatomy and topography. (A) We co-registered dense 1111 mappings from monkeys R and F (black dots; Materials and Methods), and then confirmed that physiologically- 1112 identified non-SC sites were at appropriate anatomical locations relative to the SC (Materials and Methods). Each dot 1113 represents a single electrode penetration reaching either the most superficial SC laminae (black) or non-SC sites 1114 (colors). The colored sites are SC-neighboring structures (legend). (B) Histological sections were aligned using an 1115 electrolytic lesion and then manually traced to generate a 3-dimensional structure (Materials and Methods). The lesion 1116 was placed 100 µm rostro-medially to the last visual RF in the SC. (C) The data were then aligned to a standardized 1117 postmortem macaque MRI sequence (68) (Materials and Methods). (D) This allowed us to map our electrode 1118 penetrations from A to 3-dimensional structure, and to confirm the anatomical landmarks based on SC-neighboring 1119 structures (see Movie S1). (E) We used our new SC surface topography model (Figs. 3-4) to describe 3-dimensional 1120 SC surface topography on a standard macaque MRI (see Movie S2). The left SC topography shown is just a mirror 1121 image of the right SC topography that we generated from our data. Data Table S1 lists all 3-dimensional coordinates 1122 for the shown iso-eccentricity and iso-direction lines in the right SC as a reference for future uses of the 3-dimensional 1123 model. 1124

51 bioRxiv preprint doi: https://doi.org/10.1101/554121; this version posted February 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

1125

1126 1127 Figure S7 Orderly topographic organization within SC foveal visual representation even in awake monkeys. We took 1128 a contiguous series of 22 back-to-back awake-monkey recording experiments, in which we systematically sampled 1129 within the rostral region of a single SC (the right SC) of a single monkey (monkey N). In the left panel, we plotted 1130 penetration locations within the recording chamber (the chamber was placed on the midline and tilted 35 deg posterior 1131 of vertical in this animal; Materials and Methods), and we color-coded the penetration locations according to the 1132 preferred visual eccentricities encountered in the most superficial SC laminae. The preferred eccentricities are plotted 1133 in visual coordinates in the right panel (using a logarithmic eccentricity scale). The colored lines in the left panel are 1134 linear regression lines for each color coding of penetration location, demonstrating orderly clustering of iso- 1135 eccentricity sites, and with an anatomical orientation (relative to the rostral-caudal axis) similar to that seen in the 1136 anesthetized animals (Fig. 3A-D). We also observed that medial sites represented upward directions from horizontal 1137 and lateral sites represented downward directions. Note that a direct comparison of the left panel to Fig. 3 is not 1138 appropriate because of the different penetration angles in the two cases. 1139

52 bioRxiv preprint doi: https://doi.org/10.1101/554121; this version posted February 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

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1142 1143 Figure S8 Recasting interpretations of SC efferent projections to the oculomotor periphery. (A) Besides comparisons 1144 to primary visual cortex (V1), a potential source of afferent input to the SC (Fig. 3F), we also explored the implications 1145 of larger foveal magnification on interpreting efferent SC projections. The figure, adapted with permission from (38), 1146 shows SC projection densities (gray dots) to the lateral rectus eye muscle (driving horizontal eye movements). Blue 1147 is Grantyn et al.’s (38) estimate of topography, based on (65), and the diagonal grid is their binning of tissue for the 1148 measurements in C. HM means horizontal meridian. The red arrow shows the 2-deg eccentricity line according to our 1149 more complete measurements of SC topography (Figs. 3-4, S6, S7), if our map was aligned at the origin with the 1150 Robinson map alignment (as in Fig. 3D); this demonstrates how the interpretation of raw cell densities (gray dots) can 1151 be grossly misestimated. (B) This is better illustrated when our map is superimposed in red, again when the origin was 1152 aligned to the same origin of the blue map. (C) Histograms of the cell densities from A, B along the horizontal 1153 meridian. With the original map placement (black horizontal axis of eccentricity), it may appear that the central 5 deg 1154 of SC representation are a distinct zone because of the bimodal distribution dip near 5 deg in the black horizontal axis. 1155 However, with our more complete mapping of SC topography, the distinct zone transition in cell densities may 1156 delineate a much smaller eccentricity (red arrow). 1157

53 bioRxiv preprint doi: https://doi.org/10.1101/554121; this version posted February 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

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1160 1161 Figure S9 SC activation when tiny fixational eye movements shift retinal images. The combination of foveal 1162 magnification (Figs. 3, 4) and eye movements (Figs. 5, 6) means that even small foveal stimuli can cause significant 1163 activation waves. The figure shows how the retinal image of a small foveal spot gets moved around by fixational eye 1164 movements and what this means in neural tissue coordinates. (A) Retinotopic stimulus position in one example trial 1165 of a small stationary spot (e.g. Fig. 5A). (B) The left panel shows the motion trajectory (blue) from A in retinotopic 1166 visual field coordinates. The spot was initially place at 0.4 deg before being shifted around by fixational eye 1167 movements, and the small red circle delineates 2 deg. Relative to the entire visual field (left panel), the motion 1168 trajectory (blue) was barely visible. The right panel magnifies the central 2 deg to highlight the small motion. (C) The 1169 motion of the spot on SC tissue as per the classic model of (37). The blue circle demonstrates an estimate of the active 1170 population (e.g. Fig. 4) at a specific time during the trial. (D) A more accurate depiction of stimulus trajectory from 1171 the same trial based on our dense mapping of SC foveal topography (Figs. 3, 4). A simple foveal stimulus can activate 1172 up to ~1 mm of SC tissue due to small fixational eye movements. (E-H) Same for another example trial. (I-L) Same 1173 for another example trial. Note how the edge of the active population (red dashed vertical line) can reach a distance 1174 greater than 1/4-1/3 of the entire SC rostral-caudal extent. Also note that in real neural dynamics, there can be even 1175 longer range interactions than simply stimulus position (42, 43). SC maps were rotated as in Fig. 4 such that the 1176 eccentricity dimension was on the horizontal dimension. 1177

54 bioRxiv preprint doi: https://doi.org/10.1101/554121; this version posted February 18, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license.

1178 Movie S1 1179 Results of Fig. S6D after aligning our penetration locations with anatomical locations of in the SC. The color coding 1180 for non-SC sites is the same as that in Fig. S6A. 1181

1182 Movie S2 1183 Results of Fig. S6E. Iso-eccentricity and iso-direction lines when project onto the 3-dimensional anatomical SC 1184 structure. Data Table S1 lists all 3-dimensional locations in this movie for future uses of our revised view of SC 1185 topography. The left SC iso-eccentricity and iso-direction lines were reflected from measurements of the right SC. 1186

1187 Data Table S1 1188 A Microsoft Excel file (related to Fig. S6 and Movie S2) containing tables of x, y, and z coordinates for the right SC’s 1189 anatomical coordinates along with individual iso-eccentricity and iso-direction lines. The file contains a table for iso- 1190 eccentricity lines and a table for iso-direction lines. The file also contains additional tables with coordinates for the 3- 1191 dimensional anatomical SC surface (for generating Movie S2), as a resource for future uses of our SC surface 1192 topography. All measurements are in millimeters (mm) relative to the anterior commissure, as explained in the file 1193 (68). 1194 1195

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