Grid cell symmetry is shaped by environmental geometry

Grid cells represent an animal’s location by firing in multiple fields arranged in a striking hexagonal array. Such an impressive and constant regularity prompted suggestions that grid cells represent a universal and environmental-invariant metric for navigation. Originally the properties of grid patterns were believed to be independent of the shape of the environment and this notion has dominated almost all theoretical grid cell models. However, several studies indicate that environmental boundaries influence grid firing, though the strength, nature and longevity of this effect is unclear. Here we show that grid orientation, scale, symmetry and homogeneity are strongly and permanently affected by environmental geometry. We found that grid patterns orient to the walls of polarized enclosures such as squares, but not circles. Furthermore, the hexagonal grid symmetry is permanently broken in highly polarized environments such as trapezoids, the pattern being more elliptical and less homogeneous. Our results provide compelling evidence for the idea that environmental boundaries compete with the internal organization of the grid cell system to drive grid firing. Notably, grid cell activity is more local than previously thought and as a consequence cannot provide a universal spatial metric in all environments.

[1]  May-Britt Moser,et al.  The entorhinal grid map is discretized , 2012, Nature.

[2]  M. Moser,et al.  Representation of Geometric Borders in the Entorhinal Cortex , 2008, Science.

[3]  K. Jeffery,et al.  Experience-dependent rescaling of entorhinal grids , 2007, Nature Neuroscience.

[4]  Mark C. Fuhs,et al.  A Spin Glass Model of Path Integration in Rat Medial Entorhinal Cortex , 2006, The Journal of Neuroscience.

[5]  R. Morris,et al.  Place navigation impaired in rats with hippocampal lesions , 1982, Nature.

[6]  J. O’Keefe,et al.  Grid cell firing patterns signal environmental novelty by expansion , 2012, Proceedings of the National Academy of Sciences.

[7]  K. Cheng A purely geometric module in the rat's spatial representation , 1986, Cognition.

[8]  K. Jeffery,et al.  The Boundary Vector Cell Model of Place Cell Firing and Spatial Memory , 2006, Reviews in the neurosciences.

[9]  Jonathan R. Whitlock,et al.  Fragmentation of grid cell maps in a multicompartment environment , 2009, Nature Neuroscience.

[10]  J. O’Keefe,et al.  Neural Representations of Location Composed of Spatially Periodic Bands , 2012, Science.

[11]  Jonathan W. Kelly,et al.  The shape of human navigation: How environmental geometry is used in maintenance of spatial orientation , 2008, Cognition.

[12]  G. Buzsáki,et al.  Memory, navigation and theta rhythm in the hippocampal-entorhinal system , 2013, Nature Neuroscience.

[13]  R U Muller,et al.  Head-direction cells recorded from the postsubiculum in freely moving rats. I. Description and quantitative analysis , 1990, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[14]  T. Hafting,et al.  Microstructure of a spatial map in the entorhinal cortex , 2005, Nature.

[15]  N. Burgess Grid cells and theta as oscillatory interference: Theory and predictions , 2008, Hippocampus.

[16]  J. O’Keefe,et al.  Geometric determinants of the place fields of hippocampal neurons , 1996, Nature.

[17]  Ila R Fiete,et al.  What Grid Cells Convey about Rat Location , 2008, The Journal of Neuroscience.

[18]  C. Gallistel The Organization of Action: A New Synthesis , 1982 .

[19]  J. O'Keefe,et al.  The hippocampus as a spatial map. Preliminary evidence from unit activity in the freely-moving rat. , 1971, Brain research.

[20]  J. O’Keefe,et al.  How environment geometry affects grid cell symmetry and what we can learn from it , 2014, Philosophical Transactions of the Royal Society B: Biological Sciences.

[21]  Thomas J. Wills,et al.  Development of the Hippocampal Cognitive Map in Preweanling Rats , 2010, Science.

[22]  M. Hasselmo Grid cell mechanisms and function: Contributions of entorhinal persistent spiking and phase resetting , 2008, Hippocampus.

[23]  Bruce L. McNaughton,et al.  An Information-Theoretic Approach to Deciphering the Hippocampal Code , 1992, NIPS.