Over the course of the first 10 sessions prior to surgery, the number of errors the animals made after the first correct trial in each block of trials decreased significantly over sessions (F(9,99) = 5.26, p<0.001, ${\eta }_p^2$ = 0.32; Figure 2A solid line). The time the rats took to complete each trial once they had located the rewarded goal in a block of trials also decreased significantly across sessions (F(9,99) = 6.87, p<0.001, ${\eta }_p^2$ = 0.38; Figure 2B solid line). In contrast, neither the number of errors per session (F(9,99) = 1.80, p>0.05), nor the time per trial (F(9,99) = 1.95, p>0.05) on trials prior to finding the rewarded goal box in each block changed significantly over sessions (Figure 2A and B respectively, dashed lines). Together, these results suggest that the rats could remember the last rewarded goal and learned to apply the win-stay, lose-shift rule, but that their efficiency in searching for the new goal location at the beginning of each block did not improve significantly across sessions.

Figure 2

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Consistent with this, the rats navigated from the start box to a goal box significantly faster once they were aware of the reward location within each block of trials (F(1,11) = 25.83, p<0.001, ${\eta }_p^2$ = 0.70). Across all sessions, the rats averaged 9.08 s (S.D. = 6.19 s) to travel from the start box to the end of the maze on trials before they had identified the goal box which contained reward. Once the rewarded goal box had been visited, travel time on later trials in that block decreased to 5.38 s (S.D. = 3.48 s).

During training the animals made a greater number of errors on the trials when Routes 2 or 3 to the Centre Goal Box were rewarded than on trials when the outer routes (Routes 1 or 4) to the Left and Right Goal Boxes, respectively, were rewarded (t(9) = 4.53, p<0.005, paired t-test, see Figure 2C). This difference decreased across the training period (inner/outer goal x session interaction: F(9,99) = 2.99, p<0.005, ${\eta }_p^2$ = 0.21; Figure 2D).

We sought to define the nature of the errors which rats made after finding the location of the food reward in each block. An error where the rat took Route 1 to the Left Goal Box when Route 2 to the Centre Goal Box was rewarded can be interpreted as a similar form of navigation error as taking Route 2 to the Centre Goal Box when Route 1 to the Left Goal Box was rewarded. Both results may reflect an inability to discriminate between those two reward locations or routes. Figure 2E shows the distribution of post-reward errors when grouped into the six possible pairs of these confusion errors. From this figure it is clear that the rats made more errors between the two routes to the same goal (Routes 2 and 3 to the Centre Goal) as opposed to any other route pairs (F(5,55) = 11.75, p<0.001, ${\eta }_p^2$ = 0.52). Post-hoc multiple comparison tests confirmed Routes 2 and 3 were confused more than any other route pair (p<0.05 in all cases, with Sidak correction).

Electrode tracks confirmed placement of the electrodes in the CA1 region of the HPC (Figure 9). The final electrode placement for one of the eight animals was less obvious due to tissue damage near the implant site. For this animal, part of the electrode track was seen in the cortex above the HPC and appeared to have descended at the correct ML and AP coordinates, and complex spikes and theta oscillations were observed. The neurons recorded from this animal which passed our criteria for place cells in the maze apparatus did not differ from the other animals in terms of isolation distance, l-ratio, average firing rate, maximum firing rate (found in the firing rate map), width of waveform or spatial information content (p>0.05 in all cases, Exact Kolmogorov-Smirnov tests). Thus, this rat’s data were included in the analyses above.

Figure 9

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Previous studies have shown that when a well-trained rat runs through the common segment of a maze on its way to or from different destinations, clear modulation of hippocampal place cell firing rates is observed (e.g., Wood et al., 2000; Frank et al., 2000; Ferbinteanu and Shapiro, 2003; Bower et al., 2005; Ji and Wilson, 2008; Pastalkova et al., 2008; Ferbinteanu et al., 2011; Catanese et al., 2014; Ito et al., 2015). In many cases, however, it is unclear what this differential firing represents. In a continuous maze, differential firing appears to represent previous locations early in the common stem of the maze, and intended destinations later in the common stem (Catanese et al., 2014). In discrete trial tasks, where the animal is picked up and returned to a start box on each trial, the finding that place cells are active on journeys to one goal box and not active for journeys to other goal boxes has been interpreted as an encoding of the animal’s intended destination (Ainge et al., 2007, 2012).

However, an alternative explanation is also plausible. In the Ainge et al. (2007) experiment, as in other studies, animals were well-trained. The rats ran rapidly to the rewarded goal box with little hesitation along the route. Thus the modulation of place cell firing observed in this task might not represent the intended destination per se, but rather a read-out of a specific trajectory sequence (as in Pastalkova et al. [2008]). To differentiate between these possibilities, we tested animals on a task where two different routes led to the same goal location. Differential place cell firing on the overlapping portions of these routes would suggest that such activity encodes specific routes. Similar firing on the two routes would be consistent with the encoding of a common intended destination.

Our results demonstrate that differential firing is associated with the animal’s route and not with its final destination. Of the cells with differential firing in the start box and central stem which fired preferentially on trajectories to the Centre Goal Box, nearly 96% showed differential firing between the two potential routes. Furthermore, at an ensemble level, the firing rate of place cells in the start box or central stem was sufficient to decode the animal’s route at an above chance level, regardless of which route was taken. This indicates that the ensemble firing of place cells carries sufficient information to distinguish the two central routes to the shared goal location and is thus also route-dependent, and not goal-dependent.

A potential caveat to these findings is that we may have biased the rats’ representation towards routes by blocking one of the possible routes to the Centre Goal Box. We attempted to address this by training a second, naïve group of rats on the same task but without the transparent goal barrier. However, the majority of these animals formed a strong bias for one of the two routes to the Centre Goal Box. Thus, given the choice, the rats appeared to minimize the number of trajectories to learn, suggesting that even in the absence of a barrier, rats choose to solve the task in terms of routes, not goals. Similar navigation has been suggested in baboons, who simplify a complex jungle environment to a limited number of favourite routes (Byrne et al., 2000). The potential biasing of place cell representations is consistent with previous reports of differential place cell firing with respect to deprivation state (i.e., hunger or thirst) (Kennedy and Shapiro, 2009), spatial strategy (Ferbinteanu et al., 2011), type of reward (Allen et al., 2012), or order of non-spatial (olfactory) stimuli (Allen et al., 2016). Though route encoding is predominant in the current study, it is certainly possible that different task contingencies might yield a significant representation of individual goals.

Recent work by Ito et al. (2015) has suggested that trajectory-dependent cells are found in the nucleus reuniens, an input to CA1, and in the medial prefrontal cortex. They show that the nucleus reuniens appears necessary for the differential firing in CA1 place cells. Together with the current results, this finding implies that trajectory encoding may arise in the medial prefrontal cortex, and may be passed through the nucleus reuniens to the CA1 layer of the hippocampus.

The current results, like those of Ito et al. (2015), deal only with prospective place cell firing. Findings from (Ferbinteanu and Shapiro, 2003) indicate that retrospective firing may not reflect trajectories. They trained rats on a plus maze task, and showed that even when the animal took indirect trajectories to a goal, differential retrospective firing was observed. That is, retrospective place cell firing depended on which maze arm the rat started from, regardless of its subsequent trajectory. A likely possibility is that the hippocampus represents both where the animal is going, and where it has been. Such an account is consistent with recent demonstrations of prospective firing (e.g., Pfeiffer and Foster, 2013), and with earlier lesion studies using retrospective homing tasks (Gorny et al., 2002; Wallace and Whishaw, 2003).

A second main finding in the current experiment was that the representation of the maze environment by hippocampal place fields was non-uniform. This occurred in two domains: the distribution of place fields on the maze, and the distribution between routes.

In the current experiment, we observed a linear decrease in the frequency of active place cells from the start box to the goal locations. In previous work, place cells appear to over-represent goal locations (Markus et al., 1995; Hollup et al., 2001; Hölscher et al., 2003; Kobayashi et al., 2003; Hok et al., 2007; Dupret et al., 2010). However, in previous studies with a double-Y or continuous-T maze, over-representation of the start areas of the maze has also been observed (Ainge et al., 2007, 2012). One possibility is that in mazes where rats run overlapping routes but represent these independently, over-representation is expected for the common segments of the maze. A second, intriguing possibility is that the dorsal hippocampus represents distance to a goal, and this is more apparent in structured tasks with constrained routes. Recent findings suggest that in humans, the posterior hippocampus - which corresponds to the rodent dorsal hippocampus - exhibits more activation the farther one is from a navigational goal (Howard et al., 2014).

The second type of over-representation observed was a larger number of route-dependent cells coding specifically for the two routes to the Centre Goal Box than for routes to the two outer goal boxes. In learning the task, rats made significantly more errors when they were navigating these routes and they confused these two routes more than any other route pair. Over-representation may be the result of the recruitment of additional neural resources in the face of a difficult discrimination. The hippocampus has been implicated in the discrimination of structurally similar spatial environments (Sanderson et al., 2006; Aggleton and Pearce, 2001), and it is possible that the similarity of two central routes requires greater hippocampal resources to discriminate, yielding an increase in route specific firing.

The current study makes three contributions. First, we show that the strong modulation of place fields when rats run through a common location on their way to different destinations reflects the encoding a specific route or trajectory, and not the encoding of an intended goal per se. Second, we show that routes leading to the same goal are more difficult to discriminate than routes leading to different goals. Finally, we found that place fields over-represent the early portions of the maze, and difficult-to-discriminate routes. These results suggest that although the hippocampus represents places, the firing of place cells can also represent well-learned routes. It is possible that this representation, coupled with increased activity further from a goal, allow the animal to determine the distance and the route to a goal.

For the behavioural portion of the experiment 12 male Lister hooded rats, with an average weight of 300 g, were used as subjects. Eight of these animals were subsequently used in the electrophysiological portion of the experiment at which point they weighed approximately 400–450 g. A further eight naïve animals, with an average weight of 300 g, were used to test an alternative training protocol. All animals were housed in groups of four in standard cages, but housed individually in custom designed cages after surgery. The animals were maintained under a 12 hr light/dark cycle and testing was performed during the light phase of this cycle. Throughout testing, rats were food restricted such that they maintained approximately 90% (and not less than 80%) of their free-feeding weight. This experiment complied with the national [Animals (Scientific Procedures) Act, 1986, United Kingdom] and international [European Communities Council Directive of November 24, 1986 (86/609/EEC)] legislation governing the maintenance of laboratory animals and their use in scientific experiments. Local ethical approval was granted by the University of Edinburgh Animal Welfare and Ethical Review Board.

Microdrives were based on a modified tripod design described previously (Kubie, 1984). The drives were comprised of eight tetrodes, each of which was composed of four HML coated, 17 µm, 90% platinum 10% iridium wires (California Fine Wire, Grover Beach, CA). Tetrodes were threaded through a thin-walled stainless steel cannula (23 Gauge Hypodermic Tube, Small Parts Inc, Miramar, FL). The day before surgery and again immediately before surgery the tip of every electrode was gold plated (Non-Cyanide Gold Plating Solution, Neuralynx, MT) in order to reduce the impedance of the wire from a resting impedance of 0.7–0.9 MΩ to a plated impedance in the range of 200–300 kΩ (250 kΩ being the target impedance).

Electrodes were implanted using standard stereotaxic procedures under isoflurane anaesthesia. Hydration was maintained by subcutaneous administration of 2.5 ml 5% glucose and 1 ml 0.9% saline. Animals were also given an anti-inflammatory analgesia (small animal Carprofen/Rimadyl, Pfizer Ltd., UK) subcutaneously. Electrodes were lowered to just above the CA1 cell layer of the hippocampus (-3.5 mm AP from bregma, +2.4 mm ML from the midline, −1.7 mm DV from dura surface). The drive assembly was anchored to the skull screws and bone surface using dental cement. Animals were given at least two hours recovery in their home cage, heated to body temperature. Following this, at least one week of recovery time passed before animals were screened for cells. During this week, the animals’ food was tapered from free feeding to the pre-surgery level of restriction.

Single unit activity was observed and recorded using a 32-channel Axona USB system (Axona Ltd., St. Albans, UK). Mill-Max connectors built into the rat’s microdrive were attached to the recording system via two unity gain buffer amplifiers and a light, flexible, elasticated recording cable. The recording cable passed signals through a ceiling mounted slip-ring commutator (Dragonfly Research and Development Inc., Ridgeley, West Virginia) to a pre-amplifier where they were amplified 1000 times. The signal was then passed to a system unit; for single unit recording the signal was band-pass (Butterworth) filtered between 300 and 7000 Hz. Signals were digitized at 48 kHz and could be further amplified 10–40 times at the experimenter’s discretion. The position of the animal was recorded using infra-red LEDs fixed to the unity gain amplifiers attached to the rat’s microdrive. A ceiling mounted, infrared sensitive CCTV camera tracked the animal’s position. Rats were screened for single unit activity and for the presence of theta oscillations once or twice a day, five days a week.

The maze environment was constructed from wood and consisted of seven octagonal enclosures (25 × 25 cm with 25 cm high walls), which formed the start box, the three choice points, and the three goal boxes (Figure 1A). Seven wooden alleyways connected these enclosures; these were 20 cm long × 10 cm wide with 10 cm high walls. All alleyways and octagonal enclosures were painted blue and the maze was elevated 60 cm from the floor on wooden stools. A moveable wooden barrier (10 cm wide 25 cm tall) could be placed at the exit of the start box to confine the rat to the start box. A moveable transparent Perspex barrier (also 10 × 25 cm) could be used at one or other entrance to the central goal box to prevent the animal entering the goal box via that entrance. The maze was curtained off from the remainder of the room on the left with a large white sheet. On the right wall there was a large window blackout shutter, and on the wall in front of the maze was an upwardly directed light source. To add to the distinctiveness of the goal boxes within the maze, each contained a different object: a small grey elephant statue, a small white opaque bottle with cork stopper, and a small black and red box with slanted lid. Each goal box also had a Latin alphabet character in a different reflective colour affixed to the wall. Heavy ceramic reward dishes were placed in each goal box, directly beneath these reflective letters. The start box did not contain any objects, but an orange fluorescent star was affixed to the block which kept the animal from entering the alleyways.

The square open field environment (100 × 100 cm with 25 cm high walls) was also constructed of wood and painted black. When in use (for screening for place cells), this box was placed on top of the maze apparatus, and so was elevated 85 cm above the floor, and was surrounded by the same set of distal cues.

The current task was similar to that employed in previous experiments using a double-Y maze (Ainge et al., 2007). A trial started when the experimenter raised the wooden block holding the animal in the start box at the base of the maze. The animal then navigated through the maze to one of the three goal boxes. On any given trial, only one goal box contained reward. Rats were not permitted to return towards the start box during a trial. If the rat entered the rewarded goal box, a correct choice was scored, and it was allowed to eat the food reward (CocoPops, Kelloggs, Warrington, UK) for a minimum of three seconds. The rat was then lifted by the experimenter, placed back into the start box and allowed to finish consuming any carried food reward. If the rat entered an unrewarded goal box, an incorrect choice was scored, and the animal was returned to the start box and held there using the wooden barrier for a minimum of three seconds.

For the Centre Goal Box, one of the two entrances was blocked with a piece of clear Perspex positioned in the doorway. Thus, on trials in which the Centre Goal Box was baited, only one of the two paths from the start box to this goal box (Routes 2 or Route 3) allowed access to the reward. For trials where the Left or Right Goal Boxes were reinforced, the transparent barrier was present, but was placed on the entry to the Centre Goal Box furthest from the rewarded box (i.e., at the right entry to the Centre Box if the Left Goal Box was reinforced). This was to ensure that the choice at the final junction was between two open goal boxes.

Rats completed trials as described above until they entered the correct goal box. They were then given a further 11 trials, and in these trials the same goal box was reinforced. At the end of this first block of trials, the food was moved to a new goal box and the process was repeated (Figure 1E).

We trained an additional eight naïve rats on the same task described above in the absence of the Perspex barrier to the middle goal box. In this case, either route to the Centre Goal Box allowed access to the reward. As before, reward was available in one goal box for a block of trials, and the Centre Goal Box was reinforced for two blocks. We hoped that the rats would sample both routes at a roughly equal frequency without needing to direct their behaviour within blocks of trials to the Centre Goal Box. These rats were trained for a total of 12 sessions. Unfortunately, all of the rats rapidly developed a preference for only one route to Centre Goal Box (mean 71% of trials via preferred route), and thus this variant of the task was unsuitable for assessing differences in place cell activity between routes and goals.

After recovery from surgery, rats were screened daily for place cells in the open field apparatus. Upon the identification of place cells, an uninterrupted recording session was conducted. After a 10–15 min long recording session in the open field, rats were placed in the start box of the maze and the open field environment was removed. Rats were allowed a 60 s rest period in the start box before starting the win-stay, lose-shift task in the maze. The behavioural protocol during the maze phase was comparable to that used during pre-surgery training described above, with the exception that rats were required to make at least six correct trials within a block of trials before the reward location was changed. This was necessary to ensure adequate sampling of each trajectory. Between each trial, rats were confined to the start box for a minimum of six seconds (session mean = 9.34 s, SD = 0.62 s) in order to capture any possible differential firing which occurred there.

At the end of the recording session, the animals were removed from the maze apparatus and the electrodes were lowered in order to maximise the chance of recording from a different population of cells on the following day. No attempt was made to track cells across days, and thus a subset of the cells may have been recorded on more than one session. Rats were tested until cells were no longer observed (range 3–17 sessions).

Single unit activity was analysed offline using a Matlab script that allowed the data files to be processed by the Klustakwik spike sorting program (Kadir et al., 2013). The dimensionality of the waveform information was reduced to first principal component, energy, peak amplitude, peak time, and width of waveform. The energy of a signal x was defined as the sum of squared moduli given by the formula:

Based on these parameters, Klustakwik spike sorting algorithms were then used to distinguish and isolate separate clusters. The clusters were then further checked and refined manually using the manual cluster cutting GUI, Klusters (Hazan et al., 2006). As well as the previously mentioned features, manual cluster cutting also made use of spike auto- and cross-correlograms. Cluster quality was operationalised by calculating isolation distance (Iso-D), L_ratio, signal to noise ratio (S/N) and peak waveform amplitude, taken as the highest amplitude reached by the four mean cluster waveforms. For cluster C, containing n_c spikes, Iso-D is defined as the squared Mahalanobis distance of the n_c-th closest non-c spike to the centre of C. The squared Mahalanobis distance was calculated as:

where x_i is the vector containing features for spike i, and µ_c is the mean feature vector for cluster C. A higher value indicates better isolation from non-cluster spikes (Schmitzer-Torbert et al., 2005). The L quantity was defined as:

where i${\displaystyle \notin }$C is the set of spikes which are not members of the cluster and $CD{F}_{x_{df}^2}$ is the cumulative distribution function of the distribution with 8 degrees of freedom. The cluster quality measure, L_ratio was thus defined as L divided by the total number of spikes in the cluster (Schmitzer-Torbert and Redish, 2004). As the signal and noise are both measured across the same impedance signal to noise ratio (S/N) was defined as:

where µ is the mean of the waveform amplitude. For noise we used the noise cluster which accompanied unit spikes on that tetrode. All four quality measures were assessed for their potential impact on our analyses by comparing the values observed in differential cells to non-differential place cells and by assessing the relationship between these measures and rANCOVA F-statistic (as suggested by Schmitzer-Torbert et al., 2005).

A cluster was classified as a place cell on the maze if it satisfied the following criteria: i) the width of the waveform was >250 μs, ii) the mean firing rate on the maze was greater than 0.1 Hz but less than 5Hz (see Figure 6A) and iii) the spatial information content was greater than 0.5 b/s. Spatial information content is given by the equation:

where i is the bin number, P_i is the probability for occupancy of bin i, R_i is the mean firing rate for bin i, and R is the overall average firing rate (Skaggs et al., 1993).

Firing rate maps were used to quantify the number of distinguishable place fields on the maze. The rate maps were generated using an algorithm described by the following equations.

The Gaussian kernel used is given by:

The algorithm for calculating firing rate is then given by:

where S_i represents the positions of every recorded spike, x is the centre of the current bin, the period [0 T] is the recording session time period, y(t) is the position of the rat at time t, and h is a smoothing factor, which was set to 2.5 cm. Bins in which the rat did not explore within 5 cm of the centre were regarded as having never being visited.

If rats were aware that both Routes 2 and 3 led to the same goal box we would expect place cells to represent this location similarly regardless of the route taken there. Furthermore, we would expect higher correlations between the place cell activity in the Centre Goal Box when accessed via Route 2 and Route 3, than between activity in other pairs of boxes (e.g. the Left Box accessed via Route 1 and the Centre Goal Box when accessed by Route 2), and also that the activity in the Centre Goal Box when accessed by the two routes would more highly correlated than expected by chance.

To test this we generated a population vector, consisting of the firing rates of all place cells from all animals and sessions in the Centre Goal Box when the animals navigated using Route 2. We calculated the Spearman’s ranked correlation between this vector and the population vector for the Centre Goal Box when animals navigated using Route 3. Lastly we calculated the ranked correlation between these two vectors and vectors for the Left and Right Goal Boxes; each of these boxes was represented by only one vector as there was only one possible route to each. This analysis provides six correlation values representing the comparison of the goal box activity at the end of each route to every other one. Next we calculated the probability that each of these values could occur by chance.

To do this we calculated the ranked correlation between each of the population vectors described above with a novel vector composed of random firing rate values from each cell (in effect shuffling route identity, whilst maintaining the order of the cells) after removing those firing rates belonging to the original population vector. This process was repeated 10000 times and the probability of the original correlation value occurring by chance was then estimated as the percentile position of that value in the distribution of correlation values resulting from the shuffled correlations (using a kernel smoothed cumulative density function). This analysis tells us the probability of any two population vectors being similar by chance or in other words the likelihood that all place cells would fire similarly in two goal boxes by chance.

To assess whether place fields in areas of the maze that were traversed on more than one route were modulated by the route and/or by the goal, we focussed on activity occurring in four segments of the maze: the start box and the initial corridor or central stem (which were each common to all four routes and all three goals) and the right and left stems (each common to two routes and two goals) (Figure 1C).

The analysis for each segment was conducted only for neurons that had been identified as place cells in the maze environment, and that were active in that segment (active being defined as a mean firing >1 Hz in the maze segment on at least one of the four (or two) possible routes when all of the individual trajectories along one route were combined).

For each place cell that was active in a given segment of the maze, the firing rate in that segment was calculated for each trial (total number of spikes in segment/time in segment), together with the average x- and y- coordinates occupied by the animal for each trial, and the average velocity of the animal in that segment (total distance travelled in segment/total time spent there) for each trial. We then assessed whether firing rate differed between trials on which the animal had taken the four different routes using three different methods. See Figure 3—figure supplement 1 for an example of the parameters used in the following analyses.

Method one, reported in the main text, used a nonparametric ANCOVA described previously (Quade, 1967). Briefly, this test consists of replacing the dependent variable (DV) and covariates (COV) with ranked equivalents. A linear regression is then performed on these ranked covariates against the DV, ignoring the independent variable (IV). A one-way ANOVA is then performed on the unstandardized residuals resulting from this regression against the original IV. If this was found to be significantly modulated by the animal’s route (p<0.05) after controlling for the effects of the covariates, we conducted planned post-hoc tests. These consisted of six pairwise comparisons of the estimated marginal means between the four routes. This method was carried out in Matlab using the functions tiedrank for ranking, fitlm for the linear regression, anova1 for the one way ANOVA and multcompare for the post hoc tests.

Method two employed a similarly nonparametric form of the ANCOVA test. We conducted an ANCOVA on the firing rate data using the same DV, IV and COV as above. We then compared the F-statistic obtained from this test to a distribution of F-statistics obtained after randomly shuffling the DV and repeating the ANCOVA. We then computed a p-value by the following method:

where p is the probability that the observed F-value could have been obtained by chance, F_shuff is the distribution of F-values obtained by shuffling the DV, F_obs is the F-value obtained when testing the unshuffled DV and k is the number of shuffles conducted. For our tests we conducted 5000 shuffles.

Method three employed a Generalized Linear Model (GLM) approach instead of an ANCOVA. We conducted a linear GLM on the DV, IV and COV described above with the underlying distribution assumed to be Poisson (Di Lorenzo and Victor, 2013) and a log link function. If firing rate was found to be significantly modulated by the animal’s route (p<0.05) after controlling for the effects of the covariates, we conducted planned post-hoc tests. These consisted of six Mann-Whitney U tests comparing firing rates for every possible combination of the four routes. This method was carried out in Matlab using the functions fitglm to build the GLM and ranksum for the post hoc tests.

As an additional means of assessing the route- versus goal-related place cell firing, we tested whether the animal’s trajectory could be derived from the ensemble activity of recorded place cells. If place cells show route-dependent activity at the ensemble level, then we would expect an automated route determination method to be equally accurate for all four routes, as each would be discriminable using the ensemble. In contrast, if ensembles reflect goal anticipation, then route determination should be significantly less accurate for the two central routes, as both lead to the same goal.

Ensemble analyses were conducted separately for two segments of the maze: the start box and central stem. The animals traversed each of these zones on all trials and the trajectories within them should have remained similar regardless of which route the animals were taking. For each session and for each of these maze segments we compared the firing of all place cells on an individual trajectory (i.e. Route 1 to the Left Goal Box) to the average firing of these cells across all trajectories to each goal. In this way, we compared population vectors for every route to four, average firing rate, population vectors. However, the single trajectory being compared was not included in the calculation of its average goal vector, removing the possibility that it influenced the outcome of the assessment. To assess the similarity of each route population vector to each of the four goal vectors we used a cosine distance or cosine similarity measure defined as:

This calculation gives a value bounded between 0 and 1 if x and y are non-negative (such as firing rates). Cosine similarity can be interpreted as the cosine of the angle between two vectors, or as an alternative to the Pearson correlation that is sensitive to shifts in group values (i.e. If x is shifted to x + 1, the cosine similarity between x and y changes).

We next calculated the proportion of these comparisons which resulted in a ‘correct’ match between route vector and its corresponding goal vector and the proportion of those which suggested a similarity to one of the other goal vectors (a match was taken as the goal vector resulting in the highest similarity score). This was repeated for every session included in the analysis. In order to calculate the probability of correct matches being made by chance, we also repeated the above process 10000 times using four goal vectors where the identity of the route (but not of the contributing neuron) were shuffled, therefore disrupting any relationship between firing rate and the animal's trajectory. The probability that the proportion of correct matches made in our unshuffled analysis was the result of chance was estimated by calculating the percentile position of our observed proportion of matches in the distribution observed in the shuffled data. We did this using a kernel smoothed cumulative density function - Matlab function ksdensity. An Epanechnikov kernel was employed as it is one of the most widely used, optimal filters and we set bandwidth to the ‘default’ mode for all distributions. A brief outline of this process can be seen in Figure 7. We reasoned that if the central routes were represented more similarly (due to goal location dependent firing at an ensemble level) then we would expect an above chance level of matches between trajectories along Route 2 and the goal vector calculated for Route 3 (and vice versa) or we may expect fewer correct matches for the central routes than for the outer ones.

At the end of the experiment animals were given an overdose of pentobarbital intraperitoneally (Euthatal, Merial Animal Health Ltd., Essex, UK), and perfused with 0.9% saline solution followed by a 4% formalin solution. The brain was extracted and stored in 4% formalin for at least seven days prior to any histological analyses. The brains were sliced in 32 µm sections on a freezing microtome at −20°. These sections were stained with a 0.1% cresyl violet solution and the slice best representing the electrode track was then imaged using ImageJ software (ImageJ, NIH, Bethesda).

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

RMG is now at the Institute of Behavioural Neuroscience, Department of Experimental Psychology, University College London, London, United Kingdom. Grants: This work was supported by a grant from the UK Biotechnology and Biological Sciences Research Council (BBSRC; BB/L000040/1) to PAD.

Animal experimentation: This experiment complied with the national [Animals (Scientific Procedures) Act, 1986, United 372 Kingdom] and international [European Communities Council Directive of November 24, 1986 (86/609/EEC)] legislation governing the maintenance of laboratory animals and their use in scientific experiments.

1. Received: March 11, 2016
2. Accepted: June 9, 2016
3. Accepted Manuscript published: June 10, 2016 (version 1)
4. Accepted Manuscript updated: June 21, 2016 (version 2)
5. Version of Record published: July 12, 2016 (version 3)
6. Version of Record updated: November 19, 2020 (version 4)

© 2016, Grieves et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.