Dynamical self-organization and efficient representation of space by grid cells

Grid cells in the medial entorhinal cortex (MEC) respond when an animal occupies a periodic lattice of ‘grid fields’ in the environment. The grids are organized in modules with spatial periods, or scales, clustered around discrete values separated on average by ratios in the range 1.4–1.7. We propose a mechanism that produces this modular structure through dynamical self-organization in the MEC. In attractor network models of grid formation, the grid scale of a single module is set by the distance of recurrent inhibition between neurons. We show that the MEC forms a hierarchy of discrete modules if a smooth increase in inhibition distance along its dorso-ventral axis is accompanied by excitatory interactions along this axis. Moreover, constant scale ratios between successive modules arise through geometric relationships between triangular grids and have values that fall within the observed range. We discuss how interactions required by our model might be tested experimentally.

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Irregular distribution of grid cell firing fields in rats exploring a 3D volumetric space

Nature Neuroscience ◽

10.1038/s41593-021-00907-4 ◽

2021 ◽

Author(s):

Roddy M. Grieves ◽

Selim Jedidi-Ayoub ◽

Karyna Mishchanchuk ◽

Anyi Liu ◽

Sophie Renaudineau ◽

...

Keyword(s):

Grid Cell ◽

Lower Surface ◽

Close Packing ◽

Three Dimensions ◽

Self Organization ◽

Grid Cells ◽

Spatial Regularity ◽

Cell Firing ◽

Temporal Firing ◽

Firing Characteristics

AbstractWe investigated how entorhinal grid cells encode volumetric space. On a horizontal surface, grid cells usually produce multiple, spatially focal, approximately circular firing fields that are evenly sized and spaced to form a regular, close-packed, hexagonal array. This spatial regularity has been suggested to underlie navigational computations. In three dimensions, theoretically the equivalent firing pattern would be a regular, hexagonal close packing of evenly sized spherical fields. In the present study, we report that, in rats foraging in a cubic lattice, grid cells maintained normal temporal firing characteristics and produced spatially stable firing fields. However, although most grid fields were ellipsoid, they were sparser, larger, more variably sized and irregularly arranged, even when only fields abutting the lower surface (equivalent to the floor) were considered. Thus, grid self-organization is shaped by the environment’s structure and/or movement affordances, and grids may not need to be regular to support spatial computations.

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A geometric attractor mechanism for self-organization of entorhinal grid modules

10.1101/338087 ◽

2018 ◽

Cited By ~ 1

Author(s):

Louis Kang ◽

Vijay Balasubramanian

Keyword(s):

Entorhinal Cortex ◽

Network Models ◽

Recurrent Inhibition ◽

Modular Structure ◽

Self Organization ◽

Periodic Lattice ◽

Grid Cells ◽

Medial Entorhinal Cortex ◽

Attractor Network ◽

Discrete Values

Grid cells in the medial entorhinal cortex (MEC) respond when an animal occupies a periodic lattice of “grid fields” in the environment. The grids are organized in modules with spatial periods, or scales, clustered around discrete values separated by ratios in the range 1.2–2.0. We propose a mechanism that produces this modular structure through dynamical self-organization in the MEC. In attractor network models of grid formation, the grid scale of a single module is set by the distance of recurrent inhibition between neurons. We show that the MEC forms a hierarchy of discrete modules if a smooth increase in inhibition distance along its dorso-ventral axis is accompanied by excitatory interactions along this axis. Moreover, constant scale ratios between successive modules arise through geometric relationships between triangular grids and have values that fall within the observed range. We discuss how interactions required by our model might be tested experimentally.

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Decision letter: The self-organization of grid cells in 3D

10.7554/elife.05913.010 ◽

2015 ◽

Keyword(s):

The Self ◽

Self Organization ◽

Grid Cells

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The self-organization of grid cells in 3D

eLife ◽

10.7554/elife.05913 ◽

2015 ◽

Vol 4 ◽

Cited By ~ 17

Author(s):

Federico Stella ◽

Alessandro Treves

Keyword(s):

Three Dimensional ◽

The Self ◽

Self Organization ◽

Mutual Orientation ◽

Face Centered Cubic ◽

Full Model ◽

Grid Cells ◽

Hexagonal Close Packed ◽

Hexagonal Grids ◽

Face Centered

Do we expect periodic grid cells to emerge in bats, or perhaps dolphins, exploring a three-dimensional environment? How long will it take? Our self-organizing model, based on ring-rate adaptation, points at a complex answer. The mathematical analysis leads to asymptotic states resembling face centered cubic (FCC) and hexagonal close packed (HCP) crystal structures, which are calculated to be very close to each other in terms of cost function. The simulation of the full model, however, shows that the approach to such asymptotic states involves several sub-processes over distinct time scales. The smoothing of the initially irregular multiple fields of individual units and their arrangement into hexagonal grids over certain best planes are observed to occur relatively quickly, even in large 3D volumes. The correct mutual orientation of the planes, though, and the coordinated arrangement of different units, take a longer time, with the network showing no sign of convergence towards either a pure FCC or HCP ordering.

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