title: Grid Cell Responses in 1D Environments Assessed as Slices through a 2D Lattice.
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.
authors.affiliation: Center for Learning and Memory, University of Texas at Austin, Austin, TX 78712, USA; Department of Neuroscience, University of Texas at Austin, Austin, TX 78712, USA.
authors.forename: KiJung
authors.initials: K
authors.lastname: Yoon
authors.affiliation: Princeton Neuroscience Institute, Princeton University, Princeton, NJ 08544, USA; Bezos Center for Neural Circuit Dynamics and Princeton Neuroscience Institute, Princeton University, Princeton, NJ 08544, USA.
authors.forename: Sam
authors.initials: S
authors.lastname: Lewallen
authors.affiliation: Princeton Neuroscience Institute, Princeton University, Princeton, NJ 08544, USA.
authors.forename: Amina A
authors.initials: AA
authors.lastname: Kinkhabwala
authors.affiliation: Princeton Neuroscience Institute, Princeton University, Princeton, NJ 08544, USA; Bezos Center for Neural Circuit Dynamics and Princeton Neuroscience Institute, Princeton University, Princeton, NJ 08544, USA. Electronic address: dwtank@princeton.edu.
authors.forename: David W
authors.initials: DW
authors.lastname: Tank
authors.affiliation: Center for Learning and Memory, University of Texas at Austin, Austin, TX 78712, USA; Department of Neuroscience, University of Texas at Austin, Austin, TX 78712, USA. Electronic address: ilafiete@mail.clm.utexas.edu.
authors.forename: Ila R
authors.initials: IR
authors.lastname: Fiete
mesh_terms: D000818:Animals; D005583:Fourier Analysis; D006801:Humans; D008433:Mathematics; D008564:Membrane Potentials / Q000502:physiology*; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology*; D011157:Population Dynamics; D013028:Space Perception / Q000502:physiology*