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How do grid cells map 3D space?
See our new preprint:
https://www.biorxiv.org/content/10.1101/2020.12.06.413542v1
We wirelessly recorded mEC grid cells in rats climbing a 3D lattice.
Grid cells had fields but these formed random, not close-packed configurations!
See thread
#brain #neuroscience #GridCells
See our new preprint:
https://www.biorxiv.org/content/10.1101/2020.12.06.413542v1
We wirelessly recorded mEC grid cells in rats climbing a 3D lattice.
Grid cells had fields but these formed random, not close-packed configurations!
See thread
#brain #neuroscience #GridCells
A little background:
Theoretical work tells us that the optimal way to stack spheres in 3D is in one of 2 configurations: face-centered-cubic (FCC) or hexagonal close-packed (HCP).
https://arxiv.org/pdf/1411.2136.pdf
https://doi.org/10.7554/eLife.05913
(Thanks to @ElDuvelle for use of her marbles)
Theoretical work tells us that the optimal way to stack spheres in 3D is in one of 2 configurations: face-centered-cubic (FCC) or hexagonal close-packed (HCP).
https://arxiv.org/pdf/1411.2136.pdf
https://doi.org/10.7554/eLife.05913
(Thanks to @ElDuvelle for use of her marbles)
What has this got to do with the brain?
In 2D environments entorhinal grid cells map space with hexagonally arranged firing fields.
Here's one we recorded in an open field arena:
In 2D environments entorhinal grid cells map space with hexagonally arranged firing fields.
Here's one we recorded in an open field arena:
Grid cells could extend this 2D hexagonal firing to efficiently map 3D space with an FCC or HCP arrangement.
Alternatively, fields might extend vertically in columns, or be randomly arranged.
Alternatively, fields might extend vertically in columns, or be randomly arranged.
What did we do?
We wirelessly recorded grid cells in rats as they foraged in a 2D open field arena or climbed through a 3D lattice maze.
In the lattice rats could move in all 3 dimensions.
We wirelessly recorded grid cells in rats as they foraged in a 2D open field arena or climbed through a 3D lattice maze.
In the lattice rats could move in all 3 dimensions.
What did we find?
Grid cells were spatially modulated in 3D and they had volumetric firing fields.
These were sparser (i.e. fewer fields/m3) in the lattice than the arena.
Field size and grid spacing (distance between fields) also increased.
Grid cells were spatially modulated in 3D and they had volumetric firing fields.
These were sparser (i.e. fewer fields/m3) in the lattice than the arena.
Field size and grid spacing (distance between fields) also increased.
We took slices through the autocorrelation of each grid cell's 3D firing rate map.
For each slice we calculated how hexagonal the firing pattern was.
Different field configurations (FCC, HCP, columns) result in predictable patterns.
(I wish the real analysis was this fast)
For each slice we calculated how hexagonal the firing pattern was.
Different field configurations (FCC, HCP, columns) result in predictable patterns.
(I wish the real analysis was this fast)
The main finding:
Grid cell firing fields were not arranged in an FCC, HCP or columnar configuration!
Instead, they most closely resembled random or shuffled field configurations.
Grid cell firing fields were not arranged in an FCC, HCP or columnar configuration!
Instead, they most closely resembled random or shuffled field configurations.
An example cell.
Note the volumetric firing fields and lack of hexagonality in any of the projected maps.
All grid cells can be seen in supplementary figure 2 of the manuscript.
https://www.biorxiv.org/content/biorxiv/early/2020/12/07/2020.12.06.413542/DC1/embed/media-1.pdf?download=true
Note the volumetric firing fields and lack of hexagonality in any of the projected maps.
All grid cells can be seen in supplementary figure 2 of the manuscript.
https://www.biorxiv.org/content/biorxiv/early/2020/12/07/2020.12.06.413542/DC1/embed/media-1.pdf?download=true
In one rat (out of 7) we found evidence of planar hexagonality.
When his grid cell activity was projected down onto the XY plane a grid firing pattern appeared.
These fields were not 100% columnar though; they were disjointed in the vertical axis.
When his grid cell activity was projected down onto the XY plane a grid firing pattern appeared.
These fields were not 100% columnar though; they were disjointed in the vertical axis.
This is the most columnar example of these cells.
Note the vertically elongated fields and the hexagonal grid in the XY projections.
Note the vertically elongated fields and the hexagonal grid in the XY projections.
Grid cell directional modulation, theta & speed relationships were preserved in the lattice so the lack of a close-packed configuration was not due to disruption to these inputs.
What does this all mean?
There are a few grid cell models that do not predict FCC/HCP in 3D grid cells:
Stella and Treves (2015):
https://doi.org/10.7554/eLife.05913
Soman et al. (2018) (depending on path statistics)
https://doi.org/10.1038/s41467-018-06441-5
and Klukas et al. (2020)
https://doi.org/10.1371/journal.pcbi.1007796
There are a few grid cell models that do not predict FCC/HCP in 3D grid cells:
Stella and Treves (2015):
https://doi.org/10.7554/eLife.05913
Soman et al. (2018) (depending on path statistics)
https://doi.org/10.1038/s41467-018-06441-5
and Klukas et al. (2020)
https://doi.org/10.1371/journal.pcbi.1007796
Thus, the perfect hexagonal grid observed in 2D might not be necessary for navigation, at least not in three dimensions.
The fact that hippocampal place cells are relatively normal in the lattice maze supports this. https://doi.org/10.1038/s41467-020-14611-7
The fact that hippocampal place cells are relatively normal in the lattice maze supports this. https://doi.org/10.1038/s41467-020-14611-7
Alternatively, rats may be unable to integrate vertical movements. This would explain why we saw some evidence for horizontally planar grids
(normal XY self-motion integration, impaired in Z)
This would also explain why both grid & place cells have vertically elongated fields.
(normal XY self-motion integration, impaired in Z)
This would also explain why both grid & place cells have vertically elongated fields.
Huge thanks to @drkjjeffery for all her supervision & 3D expertise.
Selim Jedidi-Ayoub, Karyna Mishchanchuk & @AnyiLiu1 for their hard work.
Sophie Renaudineau & @ElDuvelle for lots of help & advice.
The whole IBN @EP_UCL - really a great place to do research.
Selim Jedidi-Ayoub, Karyna Mishchanchuk & @AnyiLiu1 for their hard work.
Sophie Renaudineau & @ElDuvelle for lots of help & advice.
The whole IBN @EP_UCL - really a great place to do research.
If you found this interesting also check out our 3D place cell paper:
https://doi.org/10.1038/s41467-020-14611-7
& our 3D behavior paper:
https://doi.org/10.1007/s10071-020-01432-w
& check out this excellent talk from @gilyginosar with similar grid cell results in flying bats:
https://doi.org/10.1038/s41467-020-14611-7
& our 3D behavior paper:
https://doi.org/10.1007/s10071-020-01432-w
& check out this excellent talk from @gilyginosar with similar grid cell results in flying bats:
I'll add this GIF here too, it shows a rat climbing around the large enclosure where we housed them pre-surgery. Here they had a mini-lattice for training and other climbing equipment for building muscle.
From Casali et al. (2019) https://doi.org/10.1073/pnas.1811867116
From Casali et al. (2019) https://doi.org/10.1073/pnas.1811867116
