Grid Cell Responses in 1D Environments Assessed as Slices through a 2D Lattice. Author KiJung Yoon, Sam Lewallen, Amina Kinkhabwala, David Tank, Ila Fiete Publication Year 2016 Type Journal Article Abstract Grid cells, defined by their striking periodic spatial responses in open 2D arenas, appear to respond differently on 1D tracks: the multiple response fields are not periodically arranged, peak amplitudes vary across fields, and the mean spacing between fields is larger than in 2D environments. We ask whether such 1D responses are consistent with the system's 2D dynamics. Combining analytical and numerical methods, we show that the 1D responses of grid cells with stable 1D fields are consistent with a linear slice through a 2D triangular lattice. Further, the 1D responses of comodular cells are well described by parallel slices, and the offsets in the starting points of the 1D slices can predict the measured 2D relative spatial phase between the cells. From these results, we conclude that the 2D dynamics of these cells is preserved in 1D, suggesting a common computation during both types of navigation behavior. Keywords Animals, Humans, Fourier Analysis, Models, Neurological, Neurons, Mathematics, Space Perception, Membrane Potentials, Population Dynamics Journal Neuron Volume 89 Issue 5 Pages 1086-99 Date Published 2016 Mar 02 ISSN Number 1097-4199 DOI 10.1016/j.neuron.2016.01.039 Alternate Journal Neuron PMCID PMC5507689 PMID 26898777 PubMedPubMed CentralGoogle ScholarBibTeXEndNote X3 XML