If you have yet to read the paper, which I highly recommend you do, I have summarized it at the end of this commentary.

Blake Porter

(2015) Department of Psychology & Brain Health Research Center, University of Otago, Dunedin, NZ
Correspondence: Blakeporterneuro@gmail.com.


This commentary aims to continue the discussion from Jonathan Wilson‘s article, Spatial learning by mice in three dimensions, on what may be going on in the brain of mice as they navigate the radiolarian maze. The radiolarian maze is an innovative 3D version of the traditional 2D radial arm maze. The radiolarian maze was named after the Protozoa that share the same looks, the Radiolaria.




Introduction: In essence, Wilson, Harding, Fortier, James, Donnett, Kerslake, O’Leary, Zhang, and Jeffery demonstrate that mice on the three dimensional radiolarian maze can keep in mind where they have been but fail to remember where they need to go. Performance for the spatial working memory task compared between the 3D and 2D (2D refers to the hexagon maze, not the classic maze) are quite similar.



Mazes in Wilson et al 2015

Mazes in Wilson et al 2015



However, the spatial working memory task only requires the mice visit every arm. Re-entry errors are one metric the authors use to measure performance; re-entry errors are when the mice visit an arm that has already been visited and thus is depleted of food. The mice do improve and make fewer re-entry errors with learning but still, this never reaches zero for both the working memory and reference memory cohort on both 3D and 2D mazes. These performance improvements demonstrate the mice are forming a more cohesive mental representation of the radiolarian and hexagon. The improvement in omission errors (# of arms the mice do not visit) also demonstrate mice may be building a more complete representation of the mazes with learning and error rates drop very low for both 3D and 2D across both tasks. The largest difference seen between 3D and 2D is the reference memory errors during the reference memory task where only a subset of the arms are baited. Reference memory errors occur when the mice visit an arm that has never been rewarded. After 50 training trials, in the radiolarian ~31% of arm entries were to arms that were never rewarded, compared to just ~12% for the hexagon. Thus, in both 3D and 2D, mice know where they have been (improved omission and re-entry errors) but fail to remember where it is they need to go in 3D (reference memory error).


Possible Solution for the Performance Observations: This inability to learn goal locations demonstrates to us that mice may be able to successfully carry out the working memory component of both mazes using foraging strategies similar to a Lévy walk. Foraging behaviors can be employed when food locations are unknown, such as in a new environment or when placed on a difficult radiolarian maze. Mice learn that food is never replaced after being consumed and can modify the foraging strategy such that a location where food was previously consumed is avoided (which is reflected in the data of Wilson et al. present in terms of re-entry errors). This foraging behavior would not require a very accurate representation of the complete environment (entirety of radiolarian maze), nor would it require any particular goal location to be recalled and kept in mind. In order to carry out this foraging behavior, we propose the mice form small (in area), 2D mental maps of the surface in which they can locomote for each available distal cue visible from the maze. These maps are similar to the surface coding put forward by Wilson et al. as well as the map fragment ideas put forth by (Jeffery, Jovalekic, Verriotis, & Hayman, 2013) but with some differences applicable to the radiolarian. Rather than a unified representation of the entire surface, there are multiple fragmented maps, ie if there are 4 stable distal cues the mice can form 4 small, discrete maps locked to each cue. Using these discrete maps, mice can employ a forage strategy to avoid working memory errors but as I describe below, these maps would fail when reference memory was necessary.


Discrete Surface Coding Maps: Fragmented, distal cue surface maps would represent the surface of the sphere, with arms treated as goal objects on the surface. Previous research has shown place cells can represent surfaces with pitches upwards of 45 degrees (Jeffery, Anand, & Anderson, 2006; Knierim & McNaughton, 2001) and likely aid in forming these maps on the sphere. Figure 1 illustrates my example from above with four maps representing four different sections of the radiolarian.


Possible Mental Spatial Represenation
Possible Mental Spatial Representation


From one section of the radiolarian, due to the spherical shape of the maze, the mouse may not be able to see any of the other distal cues even when scanning the distal environment (if a distal cue is on the North wall, when the mouse in near the equator on the South side of the sphere, he will not be able to see North wall). This lack of ability to see and integrate other distal cues on the radiolarian may make it very hard to form a cohesive global representation using the 4 stable maps. This is something that does not take place on purely horizontal surfaces unless there are very high walls which the mice cannot see over, which was not the case in the hexagon maze to my understanding. In a planar environment, the mouse would be able to rotate 360 degrees and see each distal cue. This may aid in the formation of a cohesive representation of the whole environment. Indeed, attentive scanning behavior in rats has been shown to facilitate the formation of stable place fields (Monaco, Rao, Roth, & Knierim, 2014). Scanning may also be particularly difficult in the lower half of the radiolarian as the mice will need to fight gravity; rearing to scan would be very energetically costly. Secondly, on the radiolarian the mice may move from East to West in which they see one cue to the left of a second cue. Then, if the mice come around the sphere from West to East, those same cues will be flipped in order. This may also contribute to the difficulty of forming a cohesive map.


Learned Foraging: We propose the mice could use a strategy akin to path-integration as Wilson et al. state may be going on to solve the working memory component of these tasks. Mice can visit each arm for a given map then move to another map when the current map is exhausted of resources. While within a discrete map, they only need to keep in mind the previous arm/s they visited within that map to avoid re-entry errors and omissions errors (wasted energy). Once one map’s resources have been exhausted, the mouse can then move along the radiolarian in a random movement pattern (similar to a Lévy walk) until he reaches another familiar map. The within map foraging strategy can then be used again. Thus, over all the mouse keeps in mind which maps he has exhausted and within map he keeps in mind which arms he exhausted. After a map is exhausted, the working memory cache of arms visited can be reset to save on memory load. This can explain the very low levels of omission errors because each arm within a map is visited once the map becomes stable. It also fits the re-entry errors; within maps re-entry errors would be low especially once each map is stable and the rule of no reward replacement is learned. However, keeping in mind each map and its reference to the other maps would be difficult on the radiolarian. This may account for the stagnant number of re-entry errors if the mice forgot they visited a particular map earlier on in the session due to being unable to associate it to more recently visited maps. Also, if particular arms do not have a stable surface map to be associated to, possibly due to lack of cues, it would be near impossible to remember and recall these arms.


The reference memory scenario: Let us presume this scenario; the mouse has enough distal cues to form enough stable, discrete surface maps covering the whole entire radiolarian (measures ~2.8m in area) and that each arm is within at least one map. However, the entire representation of the radiolarian is not cohesive; the discrete maps cannot be associated together in a cohesive manor due to the scanning problem; the lack of ability to perceive and associate all distal cues from all points on the sphere. As the mice get more experience on the task, these discrete maps become stable, and their omission errors decrease (go to each map, check each arm/s for food). Additionally, with experience, the mice learn once they consume a reward on an arm within a map they will not get rewarded again. Thus, within map re-entry errors decline. For reference memory errors to be avoided, the mouse must remember which arms are rewarded and within what map they are located and which maps he has already visited and where each map is in relation to the others. The data show the mice do improve from 56.0 ± 2.6% of arm visits consisting of those never baited (reference memory errors) down to 31.5 ± 2.9%. Yet, the hexagon group finished with 12.1 ± 1.7% reference memory errors.


Conclusion: Without the ability to form a compressive map of the entire radiolarian surface by binding together each discrete map, mice will be unable to remember and recall the location of every arm. It may be possible for the mice to remember the location of a few rewarded arms relative to their location within a map with respect to other arms and to the map’s extramaze cue. This is reflected in the improvement in reference memory errors with learning. We believe the reference memory task would likely require a complete, cohesive map of the maze so the mice can remember which maps have been exhausted in reference to the whole environment. Thus without the cohesive representation of the entire radiolarian, Wilson et al. show the higher rate of reference memory errors with non-cohesive discrete maps despite 50 training trials.



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Hafting, T., Fyhn, M., Molden, S., Moser, M.-B., & Moser, E. I. (2005). Microstructure of a spatial map in the entorhinal cortex. Nature, 436(August), 801–806. doi:10.1038/nature03721

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Jovalekic, A., Hayman, R., Becares, N., Reid, H., Thomas, G., Wilson, J., & Jeffery, K. (2011). Horizontal biases in rats ’ use of three-dimensional space. Behavioural Brain Research, 222(2), 279–288. doi:10.1016/j.bbr.2011.02.035

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Wilson, J. J., Harding, E., Fortier, M., James, B., Donnett, M., Kerslake, A., and Jeffery, K. (2015). Spatial learning by mice in three dimensions. Behavioural Brain Research, 289, 125–132. doi:10.1016/j.bbr.2015.04.035

Yartsev, M. M., & Ulanovsky, N. (2013). Representation of three-dimensional space in the hippocampus of flying bats. Science (New York, N.Y.), 340(2013), 367–72. doi:10.1126/science.1235338


Article Summary


Wilson et al., 2015 have engineered and implemented a novel, three dimensional radial arm maze, aptly named the “radiolarian” maze after Radiolaria zooplankton of similar shape. The radiolarian maze allows for adapting classic, 2 dimensional radial arm paradigms to test spatial cognition in three dimensions; an area of brain research that until recently has received little attention despite us living in a three dimension spatial world (for review, Jeffery, Jovalekic, Verriotis, & Hayman, 2013). The radiolarian maze consists of a 30cm diameter sphere at the center with 14 equidistant, 14cm long, cylindrical arms radiating off it. The maze was covered in crèpe bandage for grip and suspended by an empty, 48cm rack with the bottom vertical arm 30cm off the ground. Wilson et al. compared mice’s performance on the 3D radiolarian against two, two dimensional radial arm mazes. One of these planar mazes was the classic radial arm maze consisting of a circular central region with 13 radiating spokes. The third, referred to as the hexagon maze, had a hexagon shaped track with 2 arms radiating at each vertex, resulting in 12 total arms.

Summary of Methods:

The first was a working memory task which each arm of a given maze was baited once with no replacement after the reward was consumed. Three cohorts of 8 mice were trained for one of the three mazes. Mice were placed on a maze and had to retrieve the condensed milk at the end of each arm. It was recorded each time a mouse visited an arm, determined by when their head reached the end of an arm. Errors were recorded by two experimenters on opposite sides of the maze while the mice carried out the task. Re-entry errors were when the mice visited arms with depleted reward and omission errors were the number of arms the mice failed to ever visit. Mice were trained on one trial a day for at least 7 days or until the number of omission and re-entry errors plateaued for three days. Researchers also analyzed movement patterns for a neighboring arm bias. Mice had 7 neighboring arms on the top portion of the radiolarian and 6 on the bottom portion due to the lower vertical arm being removed from analysis (only two mice were ever brave enough to visit it and always visited it last).

The second paradigm was a reference memory task using two new cohorts of mice, one for the radiolarian and the other for the hexagon. Six arms for each mouse were assigned and these would be the only arms that were baited. For the radiolarian maze, arms of the central layer (non-vertical arms) were used and 3 top layer and 3 bottom layer arms were chosen. Mice were trained for two trials per day for over 25 days. A trial lasted for 5 minutes or when all size rewards were consumed, whichever was first. Performance was scored with working memory errors (visits to already visited arms) and reference memory errors (visits to never baited arms). Also collected were total number of arm visits, number of omission errors (in this case baited arms that were not visited), task latency, and total number of erroneous visits (commission errors).

Note for results: I left out the statistics for the sake of simplicity. You can of course find them all in the article.

Working memory Results Summary:

Four variables were analyzed of the first three days of training against the last three days, total number of visits, task latency, omission errors (total number), and re-entry error (% of total arm entries).

Radiolarian: For the radiolarian maze, no difference was found between the average total number of visits with learning. Mice did get significantly quicker at solving the maze however, with a mean latency of the last three days of 496 ± 68s vs 842 ± 40s for the first three days (900s was max time allowed). Omission and re-entry errors also decreased significantly from the first three to the last three days. Wilson et al. looked closely at movement patterns due to previous work demonstrating rats preferred to move horizontally in three dimensional environments. Mice on the radiolarian maze did not show a preference for movements, as shown by chance levels of mice visiting a horizontal arm within the same horizontal layer of neighbors. However, there was a significant preference for mice to visit neighboring arms regardless of the layer. Mice displayed learning and the capacity to successfully solve the radiolarian maze. With learning mice became faster at solving the task with decreased latencies and committed fewer errors, both omission and re-entry errors. The decrease in omission and re-entry errors show the mice can keep track of three dimensional space as they forage in it. Wilson et al. note the mice did not appear to use stereotyped choice strategies and did not show differences between horizontal and vertical movement patterns.

Classic maze: Mice employed a tactic of stereotyped movement by visiting neighboring arms with near zero omission errors. Despite introducing a barrier at the entrance of each arm on trial 5, mice quickly adapted and returned to their neighboring arm strategy. Comparing the first three days to the last, there was no significant decrease in total arm visits, omission, or re-entry errors indicating little spatial learning was taking place. Mice did become significantly faster. The hexagon maze was utilized to try and overcome the stereotyped neighbor arm strategy.

Hexagon maze: In short, comparing the first three days to the last three days, there was a significant decrease in the total number of arm visits, task latency, omission errors, and re-entry errors. These data indicate there is spatial learning for the hexagon. However, mice still showed a significant preference for moving to neighboring arms.

Comparisons: ANOVAs were used to compare the three mazes from the first three days to the last. There was significant decrease in omission errors and a significant difference between mazes. There were significantly less omissions errors from classic to radiolarian but no difference between classic and hexagon and classic and radiolarian. There was a significant decrease in re-entry errors with no difference between mazes. In regards to neighboring arm bias, there was a significant difference between mazes and it was shown mice had a significantly stronger preference for neighboring arms in the classic maze vs the radiolarian and hexagon, but no difference between the radiolarian and hexagon.

Together, these data show mice can learn a working memory task in three dimensional space on the radiolarian maze. This indicates mice have a short-term working memory of reward locations in three dimensions and this ability improves with learning. The similar error rates between the radiolarian and hexagon indicate complex spaces can reduce stereotyped movement pattern strategies to better test spatial working memory.

Reference memory task Results Summary:

Radiolarian: Comparing the first three to the last three days, total number of arm visits did not change (keep in mind the mice now are only rewarded on 6/13 arms now, this number should decrease if they are learning the reference memory) but mice did become faster at completing the maze. Average omission, commission (total erroneous visits), re-entry, and reference memory errors (visiting arms that were never baited) all significantly decreased.

Hexagon: Mice showed both significantly fewer total arm visits as well as shorter task latencies. Omission, commission, re-entry, and reference memory errors all significantly decreased comparing the first to last three days of the 25 days training.

Probe trials: Probe trials were used to rule out the possibility of olfaction cues on the reference memory task. Arms were unbaited and the mazes were rotated 180 degrees between prove trials. Probe trial performance was no different to performance of the mice by the end of training for both mazes.

Comparisons between mazes: Repeated measures ANOVA from the first three days to the last three days for the two mazes showed no difference for total visits between mazes but there was significance for interaction reflecting the decreased total visits for the hexagon maze which was not seen in the radiolarian. No difference in task latency seen. Significantly fewer omission, errors were made by mice on the hexagon compared to the radiolarian, no interaction. Significantly fewer commission errors were made between mazes and across time, reflecting the mice’s large performance improvement on the hexagon compared to on the radiolarian. Hexagon re-entry errors were significantly less and improved more than the radiolarian. Overall, fewer reference memory errors were made on the hexagon maze but there was no significant interaction for time.

Wilson et al. conclude with “Together, these data suggest that mice made fewer errors and learned more effectively on the hexagon maze than on the radiolarian maze.” Their results show mice do somewhat learn the reference memory task on the 3 dimensional radiolarian maze but their performance and rate of learning is consistently better for the 2 dimensional hexagon.

Wilson et al.’s Discussion, summary:

            Wilson et al. demonstrated mice are capable of learning in complex, three dimensional space and that spatial working memory in three dimensions is not different from a conjugate but planar radial arm maze of similar complexity (hexagon maze). However, reference memory in three dimensions appears to be impaired compared to two dimensions and, even despite similar learning rates and a lot of training time, mice never reach the same performance in three dimensions to the two dimension counterpart. The researchers fairly note the radiolarian takes more physical effort to carry out as the mice must often fight against gravity. Effort is likely one factor effecting performance but Wilson et al., 2015 propose three possible mechanisms by which the mice may be mentally representing the radiolarian to explain the discrepancies between the radiolarian and hexagon. The challenge of forming a cohesive mental map of the radiolarian is likely the largest contributor to the mice’s performance never reaching that of the hexagon maze.

Pure 3D mental map:

Wilson et al., 2015 first propose the possibility of a volumetric mental map that represents the radiolarian. They explain this map would consist of an x,y,z coordinate map with each goal (arm) represented by a unique vector. This would allow the mice to simply visit each of these locations to solve the maze successfully. The authors point out though this seems unlikely due to the neural findings of (Hayman, Verriotis, Jovalekic, Fenton, & Jeffery, 2011) and the behavioral findings from (Grobéty & Schenk, 1992) and (Jovalekic et al., 2011). Based on the above articles, Wilson et al. thought it would be likely the mice form a planar representations of the world, including for the radiolarian, and thus, “(a) confuse arms having the same horizontal coordinates and/or (b) solve the task in a planar way, visiting all the arms of one layer first followed by all the arms of the second layer.” The present findings do not give us clear evidence for the planar representations as the mice have no problem learning and solving the working memory task on the radiolarian maze compared to the hexagon. The present study also demonstrates mice do not show a preference for horizontal movement as horizontal within-layer and vertical between-layer movement were equal. If the mental representations were planar with respect to the horizontal, it would be expected mice would exhaust all arms on a horizontal layer before (a) spatially moving vertically to the other layer and (b) mentally moving to the other layer’s map. Yet, if the mice’s mental representation of the spatial world was volumetric as opposed to planar, which growing evidence shows bat’s may have (Yartsev & Ulanovsky, 2013), better performance from the mice would be expected on the radiolarian.

Two planes:

Wilson et al. postulate it may be the mice use planar representations of the world but, due to the physical effort requited for the radiolarian, mice intersperse their arm visits across planes. For example, say a mouse was on an arm on the bottom layer and consumed the reward and was on his way back to the center. If this mouse was trying to preserve energy he would likely move on the top surface of the downward facing arm such that he did not have to fight gravity as much. Once the mouse returned to the central sphere, directly ahead of him would be the arm of the above, top layer. Thus rather than using energy to change direction, the mouse moves the shortest distance and goes from lower layer to the top layer. Two planar maps on the radiolarian would mean the mice had to switch between them as they moved through the layers, this is likely very cognitively demanding. Though the hexagon maze is similarly complex, only one planar mental map would be needed. Yet, mice did learn at very similar rates on the two mazes despite having to form two planar maps for the radiolarian. Also, since the mice were unimpaired on the working memory task, it may be a problem of storing and retrieving specific locations over time that results in the reference memory performance deficits. The authors also point out the working memory task may be solved with a path-integration based strategy for representing visited and non-visited arms.

Surface Coding:

Rather than purely 3D or purely planar, Wilson et al. propose a surface-coding map, where “the mice form one large, planar map in which the surface of the spherical maze is “unwrapped” and represented in 2D coordinates. In this case, the arm positions are represented relative to the surface of the sphere (absolute vertical space is ignored) and the mice use metric information applied to the curved plane of locomotion. To me, I visualize this like textures of a video game or movie, they can be draw in two dimensions but can be wrapped around their 3D wireframe model, like so:

This example was found here: http://www.crossofthedutchman.com/2012/03/creating-character/
This example was found here: http://www.crossofthedutchman.com/2012/03/creating-character/


The authors do not rule this option out as behavioral data alone is insufficient and they propose neural recordings will provide great insight, especially recording grid cells (Hafting, Fyhn, Molden, Moser, & Moser, 2005) and head direction cells (Taube, Muller, & Ranck, 1990). Wilson et al. note they would be surprised if the surface-coding hypothesis turned out to be true due to the behavioral data they present here. It may be a possibility that the surface-coded map is difficult for the mice “to consult due to a less orderly array of arms”.
Wilson et al. conclusion:
“In our view, the most likely representational explanation is that mice form two planar maps of the two layers of arms, and need to switch between these as they move between them with consequent interference, but an alternative possibility is that they use a volumetric map which—due to its increased capacity requirements—is simply harder to form and use.” However it is mice represent the world in three dimensions, this study is a much needed stepping stone in how brains represent, remember, recall, and navigate the three dimensional world we live in.