2016
DOI: 10.1016/j.neuron.2016.01.039
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Grid Cell Responses in 1D Environments Assessed as Slices through a 2D Lattice

Abstract: SUMMARY 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 l… Show more

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Cited by 74 publications
(100 citation statements)
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“…5), where 1D patterns are considered as slices through a 2D grid 33 , gave similar results to the 1D model: gain changes lead to sub-critical (shifts) and super-critical (rescaling and remapping) responses depending on the size of the gain change, the speed of the animal, and the strength of the landmark input. An interesting distinction between the 1D and 2D models is that in the 2D super-critical regime, the landmarks also exert a pull on the attractor state that is orthogonal to the path of the animal.…”
Section: Resultsmentioning
confidence: 63%
“…5), where 1D patterns are considered as slices through a 2D grid 33 , gave similar results to the 1D model: gain changes lead to sub-critical (shifts) and super-critical (rescaling and remapping) responses depending on the size of the gain change, the speed of the animal, and the strength of the landmark input. An interesting distinction between the 1D and 2D models is that in the 2D super-critical regime, the landmarks also exert a pull on the attractor state that is orthogonal to the path of the animal.…”
Section: Resultsmentioning
confidence: 63%
“…Thus, grid cells with wider fields in the spatial environment tended also to have wider fields in the SMT, suggesting shared neural mechanisms. One possibility is that the SMT firing patterns corresponded to 1-dimensional slices through a hexagonal lattice 25 ; however, the small number of fields produced by grid cells in the SMT (typically 0–3) precluded this analysis.…”
mentioning
confidence: 99%
“…These receptive fields form a periodic triangular lattice that can be mapped to a torus 30 . Any straight-line trajectory along a primary grid axis generates a periodically repeating pattern of activity that can be mapped to a circle 31 (Figure 3a). In keeping with our assumption that overlapping responses are generated by stellate cells with overlapping inputs, we modeled the stellate-interneuron network as a ring where 'neighboring' stellate cells that fire in close spatial and temporal proximity were connected to overlapping groups of interneurons ( Figure 3b).…”
Section: Resultsmentioning
confidence: 99%