Posterior parietal cortex maps progress along routes sharing the same meta-structure

7 Neurons of posterior parietal cortex were recorded as rats performed a working memory 8 task within a network of intersecting paths. The specific routes utilized in task 9 performance provided opportunity to contrast responses of posterior parietal cortex sub-10 populations to linear and angular velocity with more complex responses that map route 11 progress. We found evidence for the presence of posterior parietal cortex neurons that 12 generalize in their firing patterns across routes having the same shape but opposite 13 action series. The results indicate that posterior parietal cortex has the capacity to 14 generalize the mapping of route progress independent of the specific actions taken to 15 move through those routes. We suggest that such encoding can form the basis for 16 learning the meta-structural organization of a non-random path network structure, such 17 as that commonly found in cities. 18 19

20 For many environments, travel is constrained and/or optimized by moving along 21 pathways. When multiple pathways are connected to one another, the intersections and 22 orientations across multiple pathways form what can be considered as a ‘path network’, 23 and its structure can range from highly regular to nearly random. Efficient movement 24 within environments containing a path network can be facilitated through prior 25 knowledge of the path network’s structure. For environments that have some degree of 26 repeating geometric structure, multiple different routes may have the same shape 27 despite being defined as connecting different locations or being oriented differently from 28 one another. In principle, memories for the specific shape of a route can form the basis 29 for learning the organization of a path network structure when a view of the full network 30 cannot be taken. In this conceptualization, the shapes, start and end locations, and 31 orientations of routes can be thought of as puzzle pieces which fit together to form the 32 picture of the path network. 33 Clues to how this mental process manifests in the nervous system come from 34 humans who have suffered brain damage and exhibit topographic amnesia/agnosia. 35 This syndrome is characterized by a profound inability to assess one’s location with 36 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity.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 The copyright holder for this preprintthis version posted June 17, 2024. ; https://doi.org/10.1101/2024.06.17.599318doi: bioRxiv preprint respect to landmarks in the environment, the inability to confidently navigate previously 37 learned routes, and the inability to successfully learn new routes (De Renzi et al., 1977). 38 These people often have the locus of their brain damage in or near the posterior parietal 39 cortices (PPC) (Takahashi et al., 1997; Takahashi and Kawamura, 2002). 40 In rats, neurons of PPC are known to encode progress along a route. The frame 41 of reference which these neurons respect is that of a route as having a particular shape 42 irrespective of its environmental location and orientation, independent of the scenes 43 associated with its traversal, and independent of the series of navigational actions taken 44 to complete it (Nitz, 2006; Whitlock et al., 2012). Some work suggests that neural 45 representations for progress along a path are scalable such that the same path shape 46 taken over different total distances will yield the same series of ensemble activity 47 patterns in PPC (Nitz, 2006; Nitz, 2012). Notably, PPC ensembles discriminate route 48 locations sharing the same locomotor action such as left or right turns (Nitz, 2009), and 49 PPC route progress encoding develops over just a few traversals of that route (Nitz, 50 2006). Other findings indicate that PPC neuron activity can also be explained through 51 their tuning to different linear and angular velocities integrated across differential offsets 52 in time (Alexander et al., 2022). Integration of this form can, in principle, form the basis 53 for learning route shape through locomotor experience alone. The patterns of spatial 54 tuning as described in PPC can be contrasted with the trajectory-specific encoding of 55 specific environmental locations observed for “place cells” of sub-region CA1 of 56 hippocampus (Frank and Wilson, 2001; Wood et al., 2001; Ferbinteanu and Shapiro, 57 2003). 58 The known activity patterns in PPC form a partial explanation for experience-59 based learning of a path network structure (Chrastil and Warren, 2015). It is possible, 60 though not yet observed, that shared meta-structural features of routes, such as their 61 shape, might facilitate learning of a path network structure as well. Shared meta-62 structural features of a path network could preserve the shape of a route while the 63 action sequence performed differs. In a simplified case of a squared grid environment, 64 any two complementary action sequences (e.g. four consecutive 90-degree lefts or 65 rights) generate the same shape, a rectangle, but are mirrored in orientation with 66 respect to deviations from the starting orientation. Such route shapes, reflecting the 67 navigational affordance structure of the environment, will recur from a multitude of 68 starting locations. Learning that the same shape recurs in the environment evidences 69 an understanding of the larger environment topography, such as a squared grid pattern, 70 and the navigational predictions that accompany that. While PPC neuron ensembles 71 can encode progress along routes of a particular shape as defined by an action 72 sequence, it is presently unclear to what extent the encoding of route progress more 73 generally translates onto routes that differ in their action sequence but are the same in 74 their shape. This is the key question addressed in the present work. 75 .CC-BY-NC-ND 4.0 International licenseavailable under a (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 The copyright holder for this preprintthis version posted June 17, 2024. ; https://doi.org/10.1101/2024.06.17.599318doi: bioRxiv preprint To examine PPC neuron mapping of actions versus route locations, we analyzed 76 236 identified single-units recorded from PPC as rats navigated an interconnected path-77 network, the ‘Triple-T’ maze. Performance of a working memory navigational task within 78 the environment allowed us to compare PPC responses to the linear and angular 79 velocity dynamics associated with turning actions with PPC responses to analogous 80 locations across routes that were identical in shape while differing in their constitutive 81 action sequence. We observed a sub-population of PPC neurons exhibiting opposite 82 firing patterns for pairs of routes that demand opposite action sequences. A second 83 sub-population mapped progress through pairs of routes sharing the same shape, 84 despite their differences in the locomotor action sequences they demanded. Together, 85 the findings extend prior work on spatial tuning of PPC neurons in freely-moving 86 animals to reveal spatial tuning reflective of meta-structural similarities among pathways 87 that differ with respect to actions, headings and environmental locations. We suggest 88 that this form of tuning could form the basis for the learning of environmental path-89 network structure in the absence of a top-down, map-like view. These spatial 90 representations furthermore suggest a neural basis for the conceptualization of 91 structural similarities across unique spaces. 92

93 Rats 94 Subjects were 5 male Sprague Dawley rats. From these rats, 236 PPC neurons 95 were recorded and isolated. Animals were all between 6 and 10 months old at the 96 beginning of training and were singly housed in standard plastic cages. The vivarium 97 was kept on a 12-hr light-dark cycle. Rats were initially on an ad libitum feeding 98 schedule, however after initial exposure to the recording room animals were food 99 restricted to maintain a weight between 85% and 95% baseline to maintain motivation 100 throughout the task. Experimental protocols followed all AALAC guidelines and were 101 approved by the Institutional Animal Care and Use Committee guidelines at the 102 University of California, San Diego. 103 Surgery 104 Following one month of pre-surgery training on the triple-T working memory task. 105 Rats were surgically implanted with custom built microdrives each equipped with 106 bundles of 12.5 micron tungsten wires spun in groups of 4 into tetrodes. Rats were 107 implanted unilaterally or bilaterally with microdrives positioned dorsal to PPC with wires 108 initially positioned approximately 0.5mm deep into cortex. Coordinates for implants were 109 determined through referencing the Paxinos and Watson Rat Brain Atlas (Paxinos and 110 Watson 2014). PPC coordinates relative to bregma were centered at A/P -3.8 mm, M/L 111 ±2.3 mm, D/V 0mm - 0.5mm. The microdrive implant allowed wires to be moved 112 ventrally through PPC across days in 40um increments. Tetrode locations were verified 113 .CC-BY-NC-ND 4.0 International licenseavailable under a (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 The copyright holder for this preprintthis version posted June 17, 2024. ; https://doi.org/10.1101/2024.06.17.599318doi: bioRxiv preprint post-hoc using Nissl-stained tissue by the presence of visible tracts in the tissue 114 (Supplemental Figure 2). All surgeries were performed in compliance with the 115 Institutional Animal Care and Use Committee guidelines at the University of California, 116 San Diego. 117 Triple-T Maze Environment 118 Experiments were conducted on a “triple-T” path-network maze. The track 119 (Figure 1A; 8-cm-wide pathways, overall perimeter 1.6 m × 1.25 m in length and width, 120 painted black) stood 20cm high in the middle of the recording room. The track edges 121 were 2 cm in height, allowing an unobstructed view of the environment’s boundaries 122 and associated distal visual cues. Access to certain areas of the maze was restricted by 123 placing painted black cans at key junctions. The placement of these and the locations of 124 food reward sites organized navigational behavior into 4 internal pathways each 125 measuring 140 cm in length with forced left/right turn decisions located 51 cm, 87 cm, 126 and 118 cm along each pathway (Figure 1B, C). Paths 1 and 4 and paths 2 and 3 127 demand opposite turn sequences and were mirror images of each other. Two perimeter 128 “return” routes formed a third set of mirror-image route shapes and flanked the internal 129 portions of the maze. Each was 197 cm in length and demanded two left or two right 130 turns. 131 Spatial Working Memory Behavior Task 132 Rats were habituated to the “triple-T” maze for 2 periods of about 30 minutes 133 prior to training. During the first habituation period the animal had access to the entire 134 maze without any blockers or other obstructions present. The second habituation period 135 took place the following day and utilized blockers to restrict movement to the corridors 136 used in the task (Fig 1A). Following habituation rats were trained to traverse one of the 137 four available internal pathways for food-reward. Following the collection of the food 138 reward animals learned to utilize the perimeter routes of the maze to return to the ‘main 139 stem’, the shared portion of each internal route, and begin another traversal for another 140 food reward. Rats were permitted to choose whichever route back to the ‘main stem’ 141 they preferred and were permitted to turn around only on the perimeter pathways. Rats 142 often did not change their direction however, often restricting their behavior to a single 143 direction for each position of the maze and maintaining consistent self-motion (Figure 1 144 D-I). Once animals regularly performed 80% or more non-interrupted traversals of all 145 four internal pathways a reward schedule was implemented. The reward schedule 146 started with each of the four possible internal routes being baited with a food reward at 147 the end location. The rat had to gather all the available food rewards before progressing 148 to the next ‘block’ of trials where the food rewards were replaced. Each block required 149 the rat to obtain each of the 4 potential rewards in any order and permitted for ‘error’ 150 trials where no reward was obtained, however, rats quickly learned this find-all-4 rule 151 .CC-BY-NC-ND 4.0 International licenseavailable under a (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 The copyright holder for this preprintthis version posted June 17, 2024. ; https://doi.org/10.1101/2024.06.17.599318doi: bioRxiv preprint and performed the task reliably quickly and with high accuracy (Supplemental Figure 152 1). 153 Recording Sessions 154 Each microdrive implant had one electrical interface board (EIB-16 Neuralynx) 155 connected to an amplifying headstage (20X, Triangle Biosystems). Raw signals were 156 initially amplified (50X), and high-pass filtered (>150Hz) and brought into a dedicated 157 recording computer running Plexon SortClient software. Here, the signal was digitized at 158 40kHz, band-pass filtered (0.45 – 9kHz), and amplified between 1X and 15X to fit the 159 shape of detected waveforms (for a total of 1,000X – 15,000X). Over time tetrode wires 160 were moved in 40um steps ventrally through brain tissue to maximize the number of 161 unique neural units recorded across days from each animal. Single units were identified 162 and isolated by hand using Plexon OfflineSorter software. Key waveform parameters for 163 separation were peak height, peak-valley distance, energy, average voltage, and 164 principal components. 165 Animal position data was collected at 60Hz using a ceiling-mounted camera, 166 mounted 305cm above the recording room floor. Colored LED lights affixed to the 167 implants of recorded animals were tracked using Plexon CinePlex Studio software to 168 obtain X, Y coordinates using customized MATLAB software. Lights were approximately 169 4.5cm apart and were positioned perpendicular to the heading of the animal. 170 Recordings lasted for approximately 30 minutes each during which time animals 171 performed on average 20 blocks of trials, however the total number of trials varied by 172 day. Recording sessions where rats performed under 6 blocks of trials were not 173 included in the final dataset. 174 Histology 175 Rats were perfused intracardially with a solution of 4% w/v paraformaldehyde 176 in PBS during deep anesthesia. Brains were removed and sectioned into 30um slices. 177 Brain slices were Nissl-stained to identify the location, trajectory, and depth of tetrode 178 wires in PPC. Boundaries of PPC were defined based on previous electrophysiological 179 studies and in accordance with Paxinos and Watson atlas (Paxinos and Watson, 2014). 180 Electrodes were determined to be in PPC at the time of recording from post-hoc 181 verification where the terminus location of each tetrode was identified and recorded 182 wire-movement across days was used to calculate the anatomical position for each 183 recording. All tetrodes were determined to have been in the PPC at the time of 184 recording for the units to be included in this study. 185 Identification of Clean Traversals 186 To identify traversals made on the triple-T maze that demonstrated clean and 187 uninterrupted running, custom MATLAB graphical interfaces were utilized. The user 188 .CC-BY-NC-ND 4.0 International licenseavailable under a (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 The copyright holder for this preprintthis version posted June 17, 2024. ; https://doi.org/10.1101/2024.06.17.599318doi: bioRxiv preprint defines, in space, the starting and ending ‘gates’ for each route defined for analyses. 189 From those gates, the MATLAB script automatically extracts traversals with sustained 190 running speed at or above 3cm/s between them. The user then verifies each individual 191 run to ensure there are no deviations from uninterrupted stereotyped running behavior. 192 The selection of clean runs results in the data presented in Figure 1B. Trials were 193 dropped from analysis for stalling, or non-stereotyped behavior (e.g. turning around). 194 The defined routes were the four internal routes toward potential reward sites or 195 perimeter routes leading to the internal entrance (Figure 1A). 196 Route and Space Referenced Positional Rate Vectors 197 To analyze the action and spatial correlates for each neuron, individual neuron 198 activity was mapped onto the position of each route using custom MATLAB scripts. 199 Uninterrupted traversals were used and fitted to a template with ~1cm spatial bins 200 extending from the start of each route to the end. Firing rates were then calculated for 201 each bin by dividing the total number of spikes by occupation time. Activity patterns 202 were then smoothed with a Gaussian filter (σ = 6 cm AUC = 1). 203 Like the linearized route-referenced positional rate vectors, two-dimensional 204 firing ratemaps were constructed for each neuron for the entire space of the maze for 205 the entire experiment. Tracking samples associated with a velocity at or above 3cm/s 206 the X, Y coordinates are identified and the number of spikes and occupancies for each 207 spatial bin were determined. The mapping of spike counts is divided by the mapping of 208 occupancies and multiplied by 60 to yield an estimate of spikes/second for each spatial 209 bin. This process is done for the entire experiment and averaged across each identified 210 X, Y position. Raw two-dimensional ratemaps were smoothed with a gaussian filter (σ = 211 6 cm2 AOC = 1). 212 Generalized Linear Model 213 A series of GLMs were computed to assess the impact self-motion had on the 214 activity profiles of individual neurons as rats performed the triple-T task. Linear and 215 angular velocity were chosen as predictors of firing rates as these self-motion measures 216 are often associated with PPC firing rates (e.g., Alexander et al. 2022; Whitlock et al., 217 2012). A separate “complete” GLM cGLM using linear and angular velocity as predictors 218 was constructed to model each neuron’s linearized max-normalized positional firing rate 219 vector for each internal and external route (using glmfit.m in Matlab). Coefficients were 220 calculated for both linear and angular velocities (glmval function in MATLAB) to 221 reconstruct the activity profile which was used to calculate the fit between the actual 222 firing rate vector and the cGLM output assessed using the normalized mean squared 223 error (‘NMSE’, as an output from the function ‘goodnessOfFit’ in MATLAB). Both 224 predictors had their relative contribution in modelling tested using the accuracy of the 225 GLM as a metric. To accomplish this, a partial GLM (pGLM) was fit to each neuron in 226 .CC-BY-NC-ND 4.0 International licenseavailable under a (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 The copyright holder for this preprintthis version posted June 17, 2024. ; https://doi.org/10.1101/2024.06.17.599318doi: bioRxiv preprint the same manner as above with the exclusion of either linear or angular velocity from 227 the model. Kruskall-Wallis tests with post hoc Boneferonni corrections were made 228 comparing the distribution of values derived from the pGLMs relative to their respective 229 cGLMs. To compare across groups of identified neurons, NMSE scores derived from 230 pGLMs were compared using a 2-tailed t-test. cGLM NMSE scores were used to 231 normalize the change in model fit for each pGLM, and the t-test was done on the 232 average proportional change of NMSE for the pGLM calculated for each route. 233 Correlation Analyses of Linearized Firing Rates 234 Individual neurons had their activity patterns compared across identical length 235 across the 4 internal routes and for the 2 external routes. Equal-length linearized 236 positional firing rate vectors were used to calculate a Pearson’s r value as a measure 237 for similarity. Reliability in positional firing for each route was calculated by comparing 238 the odd numbered traversals’ positional firing rates to the even numbered traversals’ 239 rates. Second, a comparison across routes was calculated for each route-pair by 240 comparing the mean firing rates from each route to each other route of equal length. 241 A distribution of correlation values under randomization was also calculated by 242 rotating the firing rate vectors for each traversal (repeated 100 times for each neuron 243 with different random degrees of rotation). This generated a larger sampling of 244 bootstrapped data from which a distribution of correlation values expected by chance 245 was determined. We took the mean plus or minus two standard deviations for each 246 control distribution to denote significance. Neurons that exhibited both above chance 247 reliability within each route, and exhibited inter-route correlations above chance were 248 classified as positive (+) neurons for each route comparison. Neurons that exhibited 249 both above chance reliability within each route, and exhibited inter-route correlations 250 below chance were classified as negative (-) neurons for each route comparison. If 251 neurons did not exhibit the above chance reliability for either route being considered, 252 the neuron was not classified as either (+) or (-) regardless of inter-route correlations. 253 254

255 Behavioral Dissociation of Locomotor Action Series from Progress Through Similarly 256 Structured Routes 257 Five adult male Sprague Dawley rats were trained to perform a spatial working 258 memory task within the ‘triple-T’ path network (Olson et al., 2019; Olson et al., 2017; 259 Figure 1A). The triple-T task entails the successive utilization of four internal pathways 260 (1-4 in Figure 1B) from a common starting point to reach each of four food reward 261 locations. Between internal path traversals, the animal returns from any of the four food 262 reward locations via either of two return pathways along the perimeter (R1, R2). Thus, 263 .CC-BY-NC-ND 4.0 International licenseavailable under a (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 The copyright holder for this preprintthis version posted June 17, 2024. ; https://doi.org/10.1101/2024.06.17.599318doi: bioRxiv preprint the task demands spatial working memory for which paths have been visited in sets of 264 four path-traversal blocks. 265 The animal is free to utilize any possible ordering of the four internal paths for 266 any given block. Delivery of food reward at the end of any internal path is predicated on 267 the animal not having returned to that location along that path prior to visiting each of 268 the four food reward locations. The animal must eventually reach all four food reward 269 locations within a given block. Therefore, ‘perfect’ blocks are composed of exactly four 270 internal path traversals. Blocks with errors are composed of both rewarded and 271 unrewarded path traversals, typically between 5 and 6 in number. 272 Each internal path is composed of three turn locations with turn 2 being forced 273 (no L versus R option). Distances between turns are the same for all four pathways, 274 yielding structural similarity in shape for specific path pairings. Each return path is 275 composed of two turn locations, both forced. Figure 1C depicts tracking data for 276 uninterrupted runs along each of the four internal and two return pathways, highlighting 277 the fact that paths 1 and 4, paths 2 and 3, and paths R1 and R2 entail movement along 278 mirror-image path shapes demanding opposite series of L versus R turns. Rats become 279 very proficient in this task (Supplemental Figure 1A, B) collecting a reward for about 280 84% of all traversals (s.d. = 6.88%). Animals utilized several strategies including the use 281 of the shorter return arm to return back to the main stem of the maze (Supplemental 282 Figure 1C mean = 0.9197 s.d. = 0.1075) and alternation at the first L/R turn site 283 common to all four internal paths (Supplemental Figure 1F mean = 0.8973 s.d. = 284 0.0916). Despite strong performance and the spontaneous development of these 285 navigational strategies, rats tended not to repeat specific internal path sequences 286 (Supplemental Figure 1D). 287 Animals navigated at consistently high speeds (Figure 1D, E) and with consistent 288 angular velocities (Figure 1G, H). The profiles of linear velocities were seen to be 289 consistent across routes (Figure 1F) whereas the profiles for angular velocities were 290 seen to differ dramatically for path 1 versus 4, path 2 versus 3 and path R1 versus R2 291 (Figure 1I). In this way, the task dissociates navigational locomotor actions in the form of 292 turns from progress through the spatial extents of similarly structured and equal-length 293 routes. 294 Positional Rate Vectors for PPC Neurons Reveal Mapping of Both Action and Route 295 Progress 296 For each isolated PPC neuron a positional firing rate vector was created for each 297 of the four internal and two return paths based on those path traversals completed 298 without interruption. Position along all four internal paths was organized into 140 spatial 299 bins approximately 3.5cm apart with bins 51, 87, and 118 representing the peaks of the 300 three turns. Similarly, position along the two return paths is organized into 196 bins with 301 .CC-BY-NC-ND 4.0 International licenseavailable under a (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 The copyright holder for this preprintthis version posted June 17, 2024. ; https://doi.org/10.1101/2024.06.17.599318doi: bioRxiv preprint bins 15 and 127 representing the peaks of the two turns. This resulting linearization of 302 the spatial firing profile organized the data for subsequent application of the rate vector 303 correlation and generalized linear modeling (GLM) analytical approaches considered 304 below. 305 For many PPC neurons, positional firing rate vectors reveal apparent tuning to 306 locomotor actions (L or R turns) as has been described in prior publications 307 (McNaughton et al., 1994; Nitz, 2006; Whitlock et al., 2012; Wilber et al., 2014; Goard et 308 al., 2016). Figure 2A depicts rate vectors for three such neurons along all six paths as 309 well as the correlations in rate vectors for all internal path combinations and the R1/R2 310 return paths combination. For neurons seeming to encode locomotor actions, rate 311 vector correlations are high for path combination 1,2 and path combination 3,4 where 312 distinction in the form of angular velocity (L/R turn type) is seen only at the very end of 313 the paths. 314 A second population of PPC neurons exhibited similar patterns of firing along all 315 four internal and along both return pathways despite their differences in L/R turning 316 series (Figure 2B). Robust firing rate variations for such neurons occurred in similar 317 locations along each route despite the action sequences differing, yielding positive 318 correlations among positional rate vectors. For some neurons with positive path-path 319 correlations, peaks in activity occur along the straight-run portions of path segments, yet 320 do not clearly align to either the linear or angular velocity profiles for those paths. 321 We defined neurons as being significantly tuned to the structure of the 322 environment based on similarity in firing patterns for path combinations 1 and 4, 2 and 323 3, and R1 and R2. For each combination, tuning to path structure was defined by inter-324 route correlation being above or below the mean and 2 standard deviations for an 325 equivalent distribution of correlation values coming from a collection of shuffled data. 326 Further, characterizing neurons as tuned to path structure demanded that they exhibit 327 stable positional rate vectors for odd-numbered versus even-numbered traversals of 328 any single path. Neurons that fell above or below two standard deviations for both 329 criteria were selected for further analyses. For all 3 path combinations, we found 330 neurons that had significantly elevated correlation values for firing rates across same-331 shaped paths despite differences in the actions taken to move through those paths 332 (referred to as ‘+’ neurons). In contrast, we also found neurons with negative 333 correlations for the same path pairings (referred to as ‘-’ neurons) consistent with tuning 334 to L or R turning behavior. 335 PPC Tuning to Self-Motion Explains Differences, but Fails to Explain Similarities in PPC 336 Neuron Activity Across Routes 337 Given that angular velocities across the path combinations 1/4, 2/3, and R1/R2 338 are negatively correlated, we considered the possibility that neurons with negative 339 .CC-BY-NC-ND 4.0 International licenseavailable under a (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 The copyright holder for this preprintthis version posted June 17, 2024. ; https://doi.org/10.1101/2024.06.17.599318doi: bioRxiv preprint positional firing rate correlations for the same path combinations might exhibit strong 340 tuning to angular velocity. Neurons with positive (‘+’) correlations could reflect tuning to 341 the similarities in shape between these same path combinations. Alternatively, positive 342 correlations might reflect tuning to linear velocities across path locations given that 343 linear velocity was positively correlated across all path combinations. 344 To examine these potential explanations for the presence of both ‘+’ and ‘-345 ‘ neurons, a generalized linear model approach was adopted (Fig 4A). Here, positional 346 firing rate vectors were modeled using linear and angular velocity as ‘predictors’ in a 347 complete model (cGLM). The normalized mean square error (NMSE) for the cGLM was 348 compared with the 2 ‘partial’ models (pGLM) created by using only linear velocity or only 349 angular velocity as predictors. Tuning to linear velocity was quantified as the difference 350 between the NMSE for the angular velocity pGLM versus the cGLM while tuning to 351 angular velocity was assessed in the same way using the difference between the cGLM 352 NMSE versus the linear velocity pGLM. 353 For each of the path combinations, figure 4B depicts the degree to which removal 354 of linear or angular velocity impacted model fitness in pGLMs for the previously defined 355 ‘+’ and ‘-‘ neuron populations. This revealed that ‘+’ and ‘-’ neurons consistently differed 356 only with respect to the strength of angular velocity as a model predictor with ‘+’ 357 neurons exhibiting significantly lower sensitivity (t-test, ***p<0.001). No significant 358 differences were observed for the ‘+’ and ‘-‘ populations in their sensitivity to linear 359 velocity. Thus, the negative correlations in positional firing rates for ‘-‘ neurons may well 360 be explained by their correlation to angular velocity (L/R turning actions) while the 361 positive correlations for ‘+’ neurons cannot be attributed to linear velocity correlations. 362

363 In this work, rats displayed excellent spatial working memory performance, 364 dynamically choosing from among multiple, interconnected pathways of a complex path 365 network in order to satisfy task demands. Such behavior set the context for examining 366 the role of PPC in encoding both route shape, and navigational actions. We compared 367 the firing of PPC neurons according to locomotor actions, as quantified by calculation of 368 linear and angular velocities, versus position along routes that were identical in 369 structure, or shape, but differed in the series of turns they demanded. Our analyses 370 focused on three pairs of paths that provided the opportunity to dissociate path shapes 371 from the series of actions required to traverse them. As expected, based on prior work 372 (e.g., McNaughton et al., 1994; Nitz, 2006; Whitlock et al., 2012), our analyses revealed 373 a population of PPC neurons with activity strongly correlated with L versus R turning 374 behavior that exhibit negative correlations of their positional rate vectors across the 375 specific path combinations chosen for analysis. Conversely, we also found a population 376 of PPC neurons with positively correlated positional rate vectors for pairs of task-defined 377 .CC-BY-NC-ND 4.0 International licenseavailable under a (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 The copyright holder for this preprintthis version posted June 17, 2024. ; https://doi.org/10.1101/2024.06.17.599318doi: bioRxiv preprint pathways that shared the same shape but were associated with opposite variations in 378 angular velocity during their traversal. 379 As assessed by a GLM approach using self-motion information (linear and 380 angular velocity) to model positional firing rates along routes, PPC neurons with high 381 negative correlations for path combinations demanding opposite action series appear to 382 have their activity patterns influenced heavily by angular velocity. A separate population 383 of PPC neurons with high positive correlations of their positional rate vectors, when 384 analyzed the same way, did not appear to have the models of their activity patterns 385 impacted by either linear or angular velocity significantly. The latter suggests that while 386 some neurons could be influenced by similar linear velocity series observed across 387 multiple routes, tuning to linear velocity cannot explain the difference between neurons 388 with positive versus negative correlations in their positional rate vectors for different 389 paths. Positively correlated neurons were not unique in the extent that linear velocity 390 could explain their activity. Overall, the results of the GLM analysis find a possible 391 explanation for negative path-path correlations as secondary to angular velocity, or 392 ‘action’, correlations. In contrast, correlation of PPC neurons to self-motion variables 393 fails to explain the recurrence of PPC neuron positional firing rate patterns that 394 generalize across same-shaped paths. 395 In prior work, PPC has often been considered to function as an ‘action-map’ 396 wherein L and R turning behavior is encoded in the activity of individual neurons, 397 influencing the production of navigational actions through projections to primary and 398 secondary motor cortices (McNaughton et al., 1994; Nitz, 2006; Nitz, 2009; Whitlock et 399 al., 2012; Akrami et al., 2018; Olson et al., 2020; Alexander and Nitz 2023). In the 400 present work, neurons with negative positional rate vector correlations for identically-401 shaped paths demanding opposite L/R turn series composed a significant proportion of 402 all PPC neurons, supporting models in which PPC functions to generate navigational 403 action plans based on visual or auditory stimuli (Scott et al., 2017) or environmental 404 locations (McNaughton et al., 1994; Whitlock et al., 2012; Olson et al., 2020). 405 PPC firing correlates to self-motion failed to explain the generalization of complex 406 positional rate vectors across routes demanding different action series. Yet, published 407 work has also demonstrated that PPC neurons can reliably encode locations along a 408 route of the same shape that recurs in different places in an environment, and which 409 demands movement through different headings, environmental locations, and visual 410 landscapes (Nitz, 2006; Nitz, 2009). Such ‘route-centered’ tuning is often complex in its 411 patterning and critical to the interpretation of the present data, robustly discriminates 412 different route locations that share the same navigational action (Nitz, 2009; Nitz, 2012). 413 This is consistent with reporting of context-dependence in PPC neurons that exhibit 414 tuning to self-motion (McNaughton et al., 1994; Whitlock et al., 2012; Harvey et al., 415 2012). 416 .CC-BY-NC-ND 4.0 International licenseavailable under a (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 The copyright holder for this preprintthis version posted June 17, 2024. ; https://doi.org/10.1101/2024.06.17.599318doi: bioRxiv preprint The present work supports and extends these findings to argue that PPC ‘route-417 centered’ firing profiles can generalize across different paths that are identical in shape, 418 but which form mirror-images of each other in the horizontal plane of the maze 419 environment and which demand opposite series of L/R turning actions. In this way, one 420 sub-population of PPC neurons can be thought of as encoding the meta-structure, or 421 topology, shared by routes. It follows that repeats in PPC ensemble activity patterns will 422 be distributed in non-random fashion within path networks, such as city grids, that afford 423 the same-shaped routes from many environmental locations (e.g., all-L-turn or all-R-turn 424 trips “around the block” for all blocks of a city grid). Based on this, we suggest that such 425 recurrence in PPC ensemble patterns, in combination with hippocampal ensemble 426 patterns discriminating all environmental locations, can form the basis for learning the 427 structural layout of an environment’s path network structure. Our results evidence the 428 co-existence of PPC neuron populations with tuning to actions and PPC neuron 429 populations with tuning to much more abstract spatial series that recur during navigation 430 in environments with non-random path-network structure which we refer to here as the 431 ‘meta-structure’ of that environment. 432 The encoding of meta-structure could be expected to be found in the brain given 433 the large-scale understanding of complex space such as that influencing route choice 434 when navigating cities of different layouts (Sevtsuk and Basu, 2022). Experience with 435 diverse meta-structures may explain then, why navigation ability is greater in individuals 436 who previously had learned city-layouts of high entropy (Coutrot et al., 2022). 437 Furthermore, the results are in accordance with human lesion studies examining 438 ‘topographic amnesia’ in which patients with PPC damage are unable to both learn new 439 routes and how they relate to the spaces they connect to (De Renzi et al. 1977). 440

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It is made The copyright holder for this preprintthis version posted June 17, 2024. ; https://doi.org/10.1101/2024.06.17.599318doi: bioRxiv preprint Figure 1 549 Components of Self-Motion During Spatial Working Memory Task 550 A) Schematic of triple-T environment configured to the find-all-4 task. Blockers, marked 551 by red X’s, were implemented to define the accessible portion of the environment. 552 B) Tracking data collected from one example recording session are shown with 553 overlapping portions of traversals separated to illustrate the labelling of individual 554 uninterrupted runs based on their terminal location. 555 C) Three path-path pairs utilize opposite action sequences. Individual internal pathway 556 pairs 1 and 4, pathway pairs 2 and 3, and the external pathway pair of R1 and R2 can 557 be considered to be mirror images of each other despite the utilization of opposite 558 turning sequences. 559 D) Individual traversals from an example recording are illustrated and color-coded with 560 respect to the animal’s measured linear velocity. 561 E) Linearized velocity-vectors for each of the routes traversed illustrated in D averaged 562 across all traversals for that recording. 563 F) Pairwise correlation values for each recording’s averaged linearized velocity vectors. 564 Demonstrating strong similarity in measured velocities across all pathway pairs. 565 G-I) Same as D-F, but for measured angular velocity. Demonstrating strong dissimilarity 566 in measured velocities for path-pairs 1&4, 2&3, and R1&R2. 567 568 569 .CC-BY-NC-ND 4.0 International licenseavailable under a (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 The copyright holder for this preprintthis version posted June 17, 2024. ; https://doi.org/10.1101/2024.06.17.599318doi: bioRxiv preprint 570 .CC-BY-NC-ND 4.0 International licenseavailable under a (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 The copyright holder for this preprintthis version posted June 17, 2024. ; https://doi.org/10.1101/2024.06.17.599318doi: bioRxiv preprint Figure 2 571 Example Parietal Cortex Neuron Responses on Triple-T Maze 572 Example neuron responses as recorded on the triple-T presented as 2-D ratemaps with 573 no-firing color-coded as dark blue, and maximal firing as indicated above each example 574 and color-coded as yellow. Below is the mean positional firing rate for each linearized 575 path (right) and the pairwise path-path correlation profile (left). 576 A) Three example neurons demonstrating putative self-motion responses. The leftmost 577 example neuron responds as the animal executes right turns. The middle and rightmost 578 example neurons increase activity as the animal executes left turns. 579 B) Three example neurons highly correlated positional rate vectors across route pairs 580 that demand opposite turn sequences (e.g., 1 vs 4, 2 vs 3, R1 vs R2). Each neuron 581 exhibits similar activity patterns across all internal routes (1-4) and across return routes 582 R1 and R2. 583 .CC-BY-NC-ND 4.0 International licenseavailable under a (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 The copyright holder for this preprintthis version posted June 17, 2024. ; https://doi.org/10.1101/2024.06.17.599318doi: bioRxiv preprint 584 .CC-BY-NC-ND 4.0 International licenseavailable under a (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 The copyright holder for this preprintthis version posted June 17, 2024. ; https://doi.org/10.1101/2024.06.17.599318doi: bioRxiv preprint Figure 3 585 Bifurcation of Firing Rate Correlations Across Dissimilar Path Pairs 586 A) 2D ratemap of another exemplar neuron exhibiting responses to self-motion 587 (specifically, left-turns). Positional mean firing rate vectors (dark blue) for each route are 588 superimposed with rate vectors generated subsequent to randomized shuffling of 589 spiking data versus tracking data (grey). 590 B) Route-route correlation profiles for the neuron of A are plotted in grey. Superimposed 591 in red box plots are the route-route correlation profiles for all ‘+’ neurons bearing 592 significantly positive correlations for route pairs that demand opposite action sequences 593 (route 1 and 4, 2 and 3, and R1 and R2). Superimposed blue box plots depict 594 correlation profiles for all ‘-‘ neurons bearing significantly negative correlations for route 595 pairs that demand opposite actions sequences. 596 C-D) Same figure layout as in A-B, but for a neuron having positive correlations for route 597 pairs demanding opposite action sequences. 598 E) Left: scatterplot of route-route positional rate vector correlations for all neurons for 599 route 1 vs 4 (x-axis) against rate vector correlations computed for odd vs even trials 600 along route 1 . Shaded regions correspond to the mean plus two standard deviations for 601 correlations derived from shuffled data. Neurons labelled in red are significantly 602 positively correlated for route 1 odd-trial versus route 1 even-trial rate vectors and for 603 route 1 versus route 4 rate vectors. Neurons in blue are significantly negatively 604 correlated for route 1 versus route 4 rate vectors, but significantly positively correlated 605 for route 1 odd-trial versus route 1 even-trial rate vectors. Middle and Right panels 606 depict the same, but for pairing of route 2 and 3 and pairing of route R1 and route R2. 607 Note that the three sets of paired routes all demand opposite action sequences, such 608 that red or ‘+’ points reflect similarity in rate vectors over routes bearing opposite action 609 sequences while blue or ‘-‘ points reflect opposite patterning in rate vectors over routes 610 demanding opposite action sequences. 611 612 .CC-BY-NC-ND 4.0 International licenseavailable under a (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 The copyright holder for this preprintthis version posted June 17, 2024. ; https://doi.org/10.1101/2024.06.17.599318doi: bioRxiv preprint 613 .CC-BY-NC-ND 4.0 International licenseavailable under a (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 The copyright holder for this preprintthis version posted June 17, 2024. ; https://doi.org/10.1101/2024.06.17.599318doi: bioRxiv preprint Figure 4 614 Linear Velocity Fails to Explain Similarity in Firing Rates Across Dissimilar Path Pairs 615 A) Ratemap for an example ‘-‘ neuron whose firing responses are strongest at R turns. 616 To the right is actual mean firing rate along route 1 (grey) along with the modelled firing 617 rate (red) for the cGLM (top graph) constructed using linear (LV) and angular velocity 618 (AV) as predictors (NMSE = 0.53, r = 0.68). The middle graph depicts the pGLM for the 619 same neuron with the model absent LV. Elimination of LV yields a 10% increase in 620 NMSE with 6% reduction in correlation between the model and actual rate vectors. The 621 bottom graph depicts the pGLM absent AV. Elimination of AV from the model yields a 622 much larger, 86% increase in NMSE with 85% reduction in correlation of actual and 623 model rate vectors. 624 B) Ratemap for an example ‘+‘ neuron with similar patterning of rate across all four 625 internal paths despite differences in their turn sequences. To the right is the actual mean 626 firing rate along route 1 (grey) along with the modelled firing rate (red) for the cGLM 627 (top, NMSE = 0.83, r = 0.41 for correlation of the actual and modelled firing rate vectors. 628 In the middle graph, the pGLM absent LV results in 13% increase in NMSE with 38% 629 reduction in correlation of the actual and modelled rate vectors. The pGLM absent AV 630 (bottom) yields a 7% increase in NMSE with a 20% reduction in correlation. 631 C) Cumulative change in NMSE was calculated across all routes for each neuron’s GLM 632 analysis. The population of neurons above, labelled (+), and below, labelled (-), were 633 tested against each other in a 2-tailed t-test to compare relative contributions of each 634 self-motion variable. Data for routes 1 and 4 (left), routes 2 and 3 (middle), and routes 635 R1 and R2 were combined. For all three route pairings, no significant difference 636 between the ‘+’ and ‘-‘ cell types is observed when LV is eliminated from the model. For 637 all three route pairings, removal of AV from the model increases NMSE significantly 638 more for ‘-‘ neurons than for ‘+’ neurons. 639 640 .CC-BY-NC-ND 4.0 International licenseavailable under a (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 The copyright holder for this preprintthis version posted June 17, 2024. ; https://doi.org/10.1101/2024.06.17.599318doi: bioRxiv preprint 641 .CC-BY-NC-ND 4.0 International licenseavailable under a (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 The copyright holder for this preprintthis version posted June 17, 2024. ; https://doi.org/10.1101/2024.06.17.599318doi: bioRxiv preprint Supplemental Figure 1 642 Details of Animal Performance on Working Memory Task 643 Compilation of performance on the find-all-4 condition. 644 A) Probability of getting a reward mean = 0.848 s.d = 0.0688. 645 B) Probability of completing a block without error mean = 0.566 s.d. = 0.1679. 646 C) Probability of choosing the shorter of two return arms mean = 0.9197 s.d. = 0.1075. 647 D) Probability of perfect blocks having stereotypy in the sequence of routes utilized. 648 Here the probability of the maximally observed route sequence in each recording is 649 used to measure the degree of stereotypy. mean = 0.4020 s.d. = 0.1730. 650 E) Probability of alternating at the first decision point on subsequent trials. mean = 651 0.8973 s.d. = 0.0916 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 .CC-BY-NC-ND 4.0 International licenseavailable under a (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 The copyright holder for this preprintthis version posted June 17, 2024. ; https://doi.org/10.1101/2024.06.17.599318doi: bioRxiv preprint 668 .CC-BY-NC-ND 4.0 International licenseavailable under a (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 The copyright holder for this preprintthis version posted June 17, 2024. ; https://doi.org/10.1101/2024.06.17.599318doi: bioRxiv preprint Supplemental Figure 2 669 Summary of Recording Site Histological Data 670 Nissl stained brain sections from each animal depicting their tetrode bundle trajectories. 671 Anatomical locations for recordings sessions included in the dataset are highlighted in 672 red. 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 .CC-BY-NC-ND 4.0 International licenseavailable under a (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 The copyright holder for this preprintthis version posted June 17, 2024. ; https://doi.org/10.1101/2024.06.17.599318doi: bioRxiv preprint 696 .CC-BY-NC-ND 4.0 International licenseavailable under a (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 The copyright holder for this preprintthis version posted June 17, 2024. ; https://doi.org/10.1101/2024.06.17.599318doi: bioRxiv preprint Supplemental Figure 3 697 Scatterplots for correlation values of individual neuron’s positional rate vectors for all 698 route combinations (x-axis) against within-route positional rate vector correlations for 699 odd versus even trials (y-axis, note that route 1/4, route 2/3, and route R1/R2 data are 700 repeated from figure 3E). Shaded regions in each correspond to the mean plus two 701 standard deviations for correlations derived from shuffled data (randomized circular 702 shuffling of rate vectors). Neurons labelled in red are significantly positively correlated 703 for both the within-path and cross path rate vector correlations. Neurons in blue are 704 significantly negatively correlated for cross-route correlations and significantly positive 705 for within-route correlations. Neuron counts for each grouping (above or below) are 706 presented above the route-route projections. 707 708 .CC-BY-NC-ND 4.0 International licenseavailable under a (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 The copyright holder for this preprintthis version posted June 17, 2024. ; https://doi.org/10.1101/2024.06.17.599318doi: bioRxiv preprint 709 .CC-BY-NC-ND 4.0 International licenseavailable under a (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 The copyright holder for this preprintthis version posted June 17, 2024. ; https://doi.org/10.1101/2024.06.17.599318doi: bioRxiv preprint