A local measure of symmetry and orientation for individual spikes of grid cells

PLoS Comput Biol. 2019 Feb 7;15(2):e1006804. doi: 10.1371/journal.pcbi.1006804. eCollection 2019 Feb.


Grid cells have attracted broad attention because of their highly symmetric hexagonal firing patterns. Recently, research has shifted its focus from the global symmetry of grid cell activity to local distortions both in space and time, such as drifts in orientation, local defects of the hexagonal symmetry, and the decay and reappearance of grid patterns after changes in lighting condition. Here, we introduce a method that allows to visualize and quantify such local distortions, by assigning both a local grid score and a local orientation to each individual spike of a neuronal recording. The score is inspired by a standard measure from crystallography, which has been introduced to quantify local order in crystals. By averaging over spikes recorded within arbitrary regions or time periods, we can quantify local variations in symmetry and orientation of firing patterns in both space and time.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Action Potentials / physiology*
  • Algorithms
  • Animals
  • Computational Biology / methods
  • Grid Cells / physiology*
  • Mammals
  • Models, Neurological*

Grant support

This study was funded by the German Ministry of Education and Research (BMBF, grant: FKZ 01GQ1201). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.